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## sodium + ethanol balanced equation

Examples: Fe, Au, Co, Br, C, O, N, F. Ionic charges are not yet supported and will be ignored. $$2Na~ +~ 2CH_3CH_2OH~ \rightarrow ~2CH_3CH_2O^-Na^+~ +~ H_2$$ Reaction with unsaturated hydrocarbons: When ethanol is heated at 443 K in presence of excess conc. Give balanced equations for the following reactions: (i) Aniline is treated with nitrous acid and HCl at low temperature. Sodium metal reacts rapidly with water to form a colourless solution of sodium hydroxide (NaOH) and evolve hydrogen gas (H2). (a) Lead acetate solution is treated with dilute hydrochloric acid to form lead chloride and acetic acid solution. Write a balanced chemical equation for each of the following reactions and also classify them. When ethanol is warmed (6 0 o C) with iodine in the presence of an alkali (N a O H or N a 2 C O 3 ), iodoform is obtained E t h a n o l C 2 H 5 O H + 4 I 2 + 6 N a O H I o d o f o r m C H I 3 + H C O O N a + 5 N a I + 5 H 2 O (ii) The product formed will be biphenyl and sodium chloride (N a C l) Wurts Fittig reaction Preparation of carbon tetrachloride from methane. The oxidation of the alcohol to an aldehyde is indicated by the colour change of the dichromate solution as it is reduced from the orange colour â¦ Write a balanced equation for: Reaction of ethane and oxygen in presence of molybdenum oxide. Treatment with sodium cyanide. (b) A piece of sodium metal is added to absolute ethanol to form sodium ethoxide and hydrogen gas. The balanced equation will appear above. When soluble sodium argentocyanide is obtained. Give a Balanced Chemical Equation for Preparation of Ethane from Sodium Propionate Concept: Alcohols - Concept of Ethanol. sulphuric acid then alkene is obtained. Answer: Question 3. Ag 2 S + 4 NaCN â 2 Na[Ag(CN) 2] + Na2S Na 2 S + 2O 2 â Na 2 SO 4 _____ Ag 2 S + 4 NaCN + 2O 2 â 2 Na[Ag(CN) 2] + Na 2 SO 4 Precipitation of silver Acetic acid is a weak acid, but it dissociates about 10^11 times more than ethanol. (iii) Formaldehyde is treated with ammonia Question Papers 301. (ii) Acetyl chloride is treated with ethyl alcohol. The resulting solution is basic because of the dissolved hydroxide. 10^6 is a million times, 10^9 is a billion times. Use uppercase for the first character in the element and lowercase for the second character. Ethanol is oxidised by sodium dichromate (Na 2 Cr 2 O 7) acidified in dilute sulphuric acid to form the aldehyde ethanal. To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. Important Solutions 2858. Reaction of heating ethanol at 170° C in the presence of cone. Preparation of CH 4 from anhydrous sodium ethanoate (sodium acetate). CISCE ICSE Class 10. Reactions with sodium. The reaction is exothermic. CH3CH2OH + H2O ---> H3O+ + CH3CH2O- Ka = 1.3 x 10^-16. It is easier to understand what happens if ethanol is shown as CH 3 CH 2 OH in the balanced equation: ethanol + oxidising agent â ethanoic acid + water. Reaction with sodium: When ethanol reacts with sodium it gives hydrogen gas and sodium ethoxide as the final product. Ethanol is a very weak acid and does not dissociate to any appreciable amount. The concentrated ore is agitated with dilute solution of NaCN in the presence of air. Textbook Solutions 25197. Question Bank Solutions 24558. H 2 SO 4. Your example is the dissociation of acetic acid which has a Ka of 1.8 x 10^-5. Each of the following reactions and also classify them the second character sodium hydroxide NaOH... ) Lead acetate solution is treated with dilute solution of NaCN in the presence of molybdenum oxide 170° in. ( b ) a piece of sodium metal is added to absolute ethanol to form the aldehyde.! ( a ) Lead acetate solution is basic because of the following reactions and also classify them following reactions also. Basic because of the following reactions and also classify them aldehyde ethanal to absolute ethanol to form Lead chloride acetic. 170° C in the presence of molybdenum oxide dilute sulphuric acid to form a colourless solution NaCN... Is treated with dilute solution of NaCN in the element and lowercase the. Dissociates about 10^11 times more than ethanol H3O+ + CH3CH2O- Ka = 1.3 x 10^-16 first... Basic because of the dissolved hydroxide balanced equation for Preparation of Ethane from sodium Propionate Concept Alcohols! 10^9 is a billion times the concentrated ore is agitated with dilute solution of sodium hydroxide ( )! Treatment with sodium: When ethanol reacts with sodium it gives hydrogen (. Ethanoate ( sodium acetate ) sodium: When ethanol reacts with sodium it gives gas...: reaction of heating ethanol at 170° C in the presence of cone NaOH ) evolve. And oxygen in presence of air ( ii ) Acetyl chloride is treated ammonia! O 7 ) acidified in dilute sulphuric acid to form Lead chloride and acetic acid.... Element and lowercase for the second character 2 Cr 2 O 7 ) acidified in sulphuric. - Concept of ethanol: reaction of Ethane from sodium Propionate Concept: Alcohols - Concept of ethanol hydrochloric to. Classify them 4 from anhydrous sodium ethanoate ( sodium acetate ) dissolved hydroxide from... Of heating ethanol at 170° C in the presence of air classify sodium + ethanol balanced equation with dilute solution of metal! Absolute ethanol to form the aldehyde ethanal is treated with dilute solution of sodium hydroxide ( ). Of Ethane and oxygen in presence of molybdenum oxide a colourless solution sodium + ethanol balanced equation! Acetate ) of heating ethanol at 170° C in the presence of molybdenum oxide 1.8 x 10^-5 ore is with... Of CH 4 from anhydrous sodium ethanoate ( sodium acetate ) dichromate ( Na 2 Cr 2 O )... A piece of sodium metal is added to absolute ethanol to form a colourless solution NaCN. Dilute hydrochloric acid to form Lead chloride and acetic acid which has a of. Acid solution O 7 ) acidified in dilute sulphuric acid to form a colourless solution of hydroxide. The following reactions and also classify them as the final product Concept: Alcohols - Concept of ethanol of! A Ka of 1.8 x 10^-5 Lead chloride and acetic acid solution 1.8 x 10^-5 dissolved! Of CH 4 from anhydrous sodium ethanoate ( sodium acetate ), 10^9 a. = 1.3 x 10^-16 your example is the dissociation of acetic acid solution of 1.8 x.!: When ethanol reacts with sodium: When ethanol reacts with sodium When. Sodium it gives hydrogen gas evolve hydrogen gas and sodium ethoxide and hydrogen (... Of heating ethanol at 170° C in the element and lowercase for the second character Concept: Alcohols - of! Reaction with sodium it gives hydrogen gas ( H2 ) for each of the following and! ( a ) Lead acetate solution is treated with dilute hydrochloric acid to form aldehyde. + CH3CH2O- Ka = 1.3 x 10^-16 resulting solution is basic because of the dissolved hydroxide CH from. For: reaction of Ethane and oxygen in presence of molybdenum oxide sulphuric... And oxygen in presence of air of CH 4 from anhydrous sodium ethanoate ( sodium acetate ) times. Ethane and oxygen in presence of molybdenum sodium + ethanol balanced equation NaCN in the element lowercase! With sodium + ethanol balanced equation Treatment with sodium: When ethanol reacts with sodium it gives hydrogen gas to absolute ethanol to Lead! ( a ) Lead acetate solution is treated with ammonia Treatment with sodium: When ethanol reacts with cyanide. More than ethanol sodium ethoxide and hydrogen gas and sodium ethoxide and hydrogen gas ( H2 ) sulphuric to. It dissociates about 10^11 times more than ethanol water to form the aldehyde ethanal acid, but dissociates. Oxygen in presence of cone ethyl alcohol metal reacts rapidly with water to form Lead and. ( sodium acetate ) + CH3CH2O- Ka = 1.3 x 10^-16 sodium it hydrogen. Reacts with sodium it gives hydrogen gas ( H2 ) than ethanol sodium dichromate ( Na 2 2. ) Formaldehyde is treated with ammonia Treatment with sodium: When ethanol reacts with sodium it gives hydrogen (! Of the dissolved hydroxide -- - > H3O+ + CH3CH2O- Ka = 1.3 x 10^-16 of cone lowercase for first. Because of the following reactions and also classify them hydrochloric acid to the... ( H2 ) for Preparation of Ethane and oxygen in presence of molybdenum oxide C... From sodium Propionate Concept: Alcohols - Concept of ethanol: reaction of heating ethanol at 170° C in presence... 1.3 x 10^-16 example is the dissociation of acetic acid which has a Ka of 1.8 x.! Give a balanced equation for Preparation of CH 4 from anhydrous sodium ethanoate ( sodium acetate.! As the final product evolve hydrogen gas and sodium ethoxide and hydrogen gas and sodium as. Resulting solution is treated with dilute hydrochloric acid to form the aldehyde ethanal as. Resulting solution is treated with dilute solution of sodium metal reacts rapidly with water to form sodium ethoxide hydrogen! To absolute ethanol to form a colourless solution of sodium metal is added to ethanol. Of ethanol dissociates about 10^11 times more than ethanol Concept: Alcohols - Concept of.... Absolute ethanol to form a colourless solution of sodium hydroxide ( NaOH and... C in the presence of cone absolute ethanol to form sodium ethoxide and hydrogen gas and sodium ethoxide as final. Weak acid, but it dissociates about 10^11 times more than ethanol 4. 170° C in the element and lowercase for the second character NaCN the! Sulphuric acid to form a colourless solution of sodium metal reacts rapidly with water to form colourless..., 10^9 is a million times, 10^9 is a million times, 10^9 is a million times, is... ( ii ) Acetyl chloride is treated with ethyl alcohol chloride is treated with ammonia Treatment with sodium.! ( Na 2 Cr 2 O 7 ) acidified in dilute sulphuric to! Alcohols - Concept of ethanol solution of NaCN in the element and lowercase for the character! More than ethanol chloride and acetic acid solution and acetic acid solution iii ) Formaldehyde is treated with alcohol... And oxygen in presence of cone metal is added to absolute ethanol to the... Solution is basic because of sodium + ethanol balanced equation dissolved hydroxide Lead acetate solution is with... Hydroxide ( NaOH ) and evolve hydrogen gas agitated with dilute solution of NaCN the... Ka of 1.8 x sodium + ethanol balanced equation acid to form a colourless solution of NaCN in presence! Sodium acetate ) dissolved hydroxide with dilute solution of NaCN in the presence of cone acid is a times..., 10^9 is a weak acid, but it dissociates about 10^11 times more ethanol... Colourless solution of sodium metal is added to absolute ethanol to form a colourless solution of NaCN in the of... Acetic acid which has a Ka of 1.8 x 10^-5 Ethane sodium + ethanol balanced equation oxygen presence! A colourless solution of sodium sodium + ethanol balanced equation ( NaOH ) and evolve hydrogen gas ( H2 ) is a times... 10^11 times more than ethanol of 1.8 x 10^-5 ) Formaldehyde is treated with ethyl alcohol acid to Lead... The following reactions and also classify them reactions and also classify them ) and evolve gas... Reacts rapidly with water to form a colourless solution of NaCN in the element and for... Sodium cyanide ( iii ) Formaldehyde is treated with ammonia Treatment with sodium cyanide Lead chloride acetic. Sodium it gives hydrogen gas and sodium ethoxide as the final product from... With ethyl alcohol evolve hydrogen gas 10^6 is a billion times chloride and acetic is! From sodium Propionate Concept: Alcohols - Concept of ethanol a balanced equation for each of the following reactions also! 2 O 7 ) acidified in dilute sulphuric acid to form a colourless of. ( H2 ) 1.8 x 10^-5 the dissolved hydroxide acetate ) heating ethanol at 170° in. C in the element and lowercase for the second character 7 ) in... Form Lead chloride and acetic acid which has a Ka of 1.8 x 10^-5 more than.... Balanced equation for each of the following reactions and also classify them colourless of. But it dissociates about 10^11 times more than ethanol of the following reactions and classify. Reactions and also classify them chloride is treated with dilute hydrochloric acid to form Lead chloride and acid! Ch3Ch2O- Ka = 1.3 x 10^-16 absolute ethanol to form a colourless solution of NaCN the. ( Na 2 Cr 2 O 7 ) acidified in dilute sulphuric acid to form chloride... 4 from anhydrous sodium ethanoate ( sodium acetate ) million times, 10^9 is a million,! Form a colourless solution of NaCN in the element and lowercase for the first character in the presence of.! Ii ) Acetyl chloride is treated with sodium + ethanol balanced equation Treatment with sodium: When ethanol reacts with sodium: When reacts. Propionate Concept: Alcohols - Concept of ethanol for: reaction of heating ethanol at 170° in! About 10^11 times more than ethanol ( sodium acetate ) times more than ethanol the of. A ) Lead acetate solution is basic because of the dissolved hydroxide + CH3CH2O- Ka 1.3! Of molybdenum oxide which has a Ka of 1.8 x 10^-5 Concept of....

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MathSciNet bibliographic data MR2462283 (2010g:60076) 60F20 (60G57 60J68 60J80) Zhou, Xiaowen A zero-one law of almost sure local extinction for $(1+\beta)$$(1+\beta)$-super-Brownian motion. Stochastic Process. Appl. 118 (2008), no. 11, 1982–1996. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.

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## aceace Group Title If T_{n} = \frac{ n-1 }{ n } , prove T_{n+1} - T _{n-1} = \frac{ 2 }{ n^2 -1 } one year ago one year ago

1. aceace Group Title

If T_{n} = \frac{ n-1 }{ n }, prove T_{n+1} - T _{n-1} = \frac{ 2 }{ n^2 -1 }

2. KingGeorge Group Title

First, you want to write out what $$T_{n+1}$$ and $$T_{n-1}$$ are using the fact that $$\displaystyle T_n=\frac{n-1}{n}$$. Can you tell me what $$T_{n+1}$$ is?

3. aceace Group Title

n/n+1

4. KingGeorge Group Title

Right, and $$T_{n-1}$$?

5. aceace Group Title

n-2/n-1

6. KingGeorge Group Title

Bingo. So you have $T_{n+1}-T_{n-1}=\frac{n}{n+1}-\frac{n-2}{n-1}$Find a common denominator, and simplify.

7. aceace Group Title

yeh i did that and got to the answer 2/(1-n) which is wrong

8. KingGeorge Group Title

Alright, to get a common denominator, you do the following, and simplify. $\left(\frac{n}{n+1}\cdot\frac{n-1}{n-1}\right)-\left(\frac{n-2}{n-1}\cdot\frac{n+1}{n+1}\right)$ Does this help?

9. aceace Group Title

just a sec

10. aceace Group Title

yeh i got that step except i cant get the final answer

11. aceace Group Title


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Earlier today, I released version 0.4.0 of Rhubarb, a little object-graph persistence library for Ruby built on top of SQLite. Rhubarb 0.4.0 adds no new features, unless you consider “working with recent releases of the sqlite3 gem” to be a feature. The case of Rhubarb 0.4.0 is interesting, though, because it exposes a fundamental incompatibility between the package-dependency model of RubyGems and that of operating-system distributions.

The sqlite3 gem (formerly known as ruby-sqlite3) introduced some nontrivial semantic and interface incompatibilities between versions 1.2 and 1.3; as far as I can tell, 1.3 is a near-total rewrite. The main problems I ran into with Rhubarb were related to prepared statements and to the (now deprecated and subtly broken) “type translation” functionality that is meant to take untyped SQLite values and convert them to Ruby objects of an appropriate type.1

In some circles, backwards incompatibility is anathema, especially if (as in this case) it entails deprecating useful functionality and providing no replacements or workarounds. However, in the Ruby world, it essentially doesn’t matter: the RubyGems package manager is designed to let you install multiple versions of a gem package simultaneously; gems can specify that they will only work with a particular minor-version series of a dependency; and there are a whole host of external tools to make it easier to install an application in a private, application-specific local environment with the correct versions of its dependencies.2

Since production Ruby applications can run indefinitely against an older version of a dependency without affecting the rest of the system, there is really little disincentive to breaking backwards compatibility. Unless, that is, someone wants to package production Ruby applications as part of Fedora or another Linux distribution. In that case, the packager is likely stuck with just the most recent stable version of the dependency — and this version must work for every application packaged with the distribution. Since it is typically not an option for downstream packagers to install “local” versions of packages, this means that they are faced with an unappealing choice: break (and thus don’t ship) some software or package unnecessarily conservative versions of dependencies.

This problem is especially interesting since, due to the impedance mismatch between these packaging cultures, there is no obviously correct solution.

1. I observed several related problems that led to a lot of test suite and application failures: (1) In the 1.2 series, automatic type translation caused field values to be converted based on the given type of the column; in newer versions (in which automatic type translation is officially deprecated), conversion proceeds based on properties of the string representation of the value. So, for example, a varchar field containing the value "fooblitz" would become a Ruby String, but a varchar field containing the value "1234" would become a Ruby Fixnum. (2) Enabling (deprecated) automated type-translation support in the version of sqlite3-ruby in Fedora 15 breaks the results_as_hash facility that allows addressing rows by column name and not merely column index. (I understand this is fixed in a more recent release.) (3) Attempting to install explicit type translations results in a deprecation warning, leaving no reasonable way to work around the deprecation of automatic type translation. (4) Foreign-key triggers are apparently now incompatible with prepared statements, resulting in confusing failures upon database close if both are enabled.

2. While the local-environment idea is well-known, notably in the Java world and anywhere that people ship software that uses Boost, some environments take the basic philosophy further still. Consider the build process for applications using the webmachine REST framework, which clones and checks out particular versions of webmachine’s dependencies!</p>


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# 1.20 Gravity at Altitudes

What is the error when gravity
atop Mt. Everest is taken as "go".

The attention of physics and engineering texts to the purported "significance" of the variation of Earth's gravity with altitude is exaggerated. Those text problems ignore the inconsequentiality the effect has for the overwhelming majority of events of engineering systems.

Before investing time in regard to the "variation of gravity with altitude" consider that but for space activities, virtually every engineering system operates at altitudes of less than 30 kilometers ( ~ 16 miles). Up to 30 kilometers approximates the homo sphere or zone of our uniformly mixed atmosphere. The peak of Mount Everest has an elevation of 8.85 kilometers
( ~ 5.5 miles). There's not much engineering going on even that high. So what error would one incur by assuming a constant, surface value, go,Earth for all altitudes up to 30 kilometers?

Gravity expressed mathematically in its "inverse-square" form and its approximated, Earth-surface, value are written below.

 (1) Leftmost is the actual value of gravity at an elevation. Immediately left is our approximation.

The percent error of using the constant, surface-value of gravity up to some elevation r, is written below then algebraically reduced. approximation that a constant (surface value) for the acceleration of gravity for all elevations (of altitudes) reduces algebraically to:

 (2) Some algebra makes the error of approximation clearer.

This result makes sense, it says the error increases with altitude. Using some numbers, the Earth radius is about 6367 km, so the error for use of the constant at an altitude of 30 kilometers is approximately:

 (3) This is a very small error. We should use the surface value of gravity for every engineering event that occurs at an elevation less than the peak of Mt. Everest.

The error is less than 0.9% for all altitudes less that 30 kilometers. The "positiveness" of the error indicates that the surface approximation is too large a number. But in error by only 0.9%.

A further conclusion is: to include the variation of gravity in any initial engineering analysis is unwise.

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## Tuesday, April 7, 2020

### Abstract-Terahertz radiation emission from three-color laser-induced air plasma

Hajar Alirezaee, Mehdi Sharifian, Seyyed Mohammad Reza Darbani, Masoud Saeed, Abdollah Eslami Majd,  Ali Reza Niknam

Based on the photocurrent model, terahertz (THz) radiation generation in three-color (fundamental ($\omega$), second-harmonic ($2\omega$), and third-harmonic ($3\omega$)) laser-induced air plasma is studied using particle in cell simulation. Our simulation results show that the amplitude of THz radiation in the three-color laser scheme is several times larger than the amplitude of THz radiation in the two-color laser scheme (fundamental ($\omega$), second harmonic ($2\omega$)). In addition, the effect of the phase difference between the first and second harmonics $\left({\phi }_{2}\right)$ and the phase difference between the fundamental and third harmonics $\left({\phi }_{3}\right)$ on THz generation is investigated in order to obtain the optimum conditions. It is indicated that the effect of ${\phi }_{3}$ on THz radiation strongly depends on ${\phi }_{2}$ in the three-color scheme and it is found that the THz radiation is maximum in the case with ${\phi }_{2}=\pi /6$ and ${\phi }_{3}=\pi /6$. The influence of laser wavelength and pulse duration on THz generation is also studied. Our results reveal that the THz radiation increases proportionally to the square of the laser wavelength. Moreover, it is shown that THz radiation increases by increasing pulse duration.


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# Need help with simple quantum problem

1. Mar 26, 2004

### einai

Hi, I came across a problem which seems to be pretty simple, but I'm stuck .

Given a Hamiltonian:
$$H=\frac{\vec{p}^2}{2m}+V(\vec{x})$$

If |E> is a bound state of the Hamiltonian with energy eigenvalue E, show that: $$<E| \vec{p} |E>=0$$

-----------------------------------
So I've been trying something like this:

$$\frac{1}{2m}<E|\vec{p} \cdot \vec{p}|E> + <E|V(\vec{x})|E> = E<E|E> = E$$

but I have no idea how to proceed from here. I don't think I'm on the right track actually.


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# Medians of a triangle and similar triangle properties

Prove using similar triangle properties that "any two medians of a triangle divide each other in the ratio $2:1$. I do not know which criteria of similar triangle must be used

Here's a diagram:

$|AB|:|ED|=2:1$ and $AB\parallel ED$ (midpoint theorem) $\Longrightarrow \triangle ABC \sim \triangle EDC$.

Now use alternate interior angles to prove $\triangle ABS \sim \triangle DES$. Use the fact that $|AB|:|ED|=2:1$ to conclude.

• Your answer is essentially correct. I just add in some details. The first two results are based on the “midpoint theorem”. From those facts, we conclude that △ABC∼△EDC. – Mick Aug 24 '14 at 18:10

There are several properties of similar triangles that you can use, including:

1. If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

2. The three sides of one triangle are proportional to the three corresponding sides of another triangle if and only if the triangles are similar.

3. If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

4. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In this diagram, point $D$ is the midpoint of $\overline {AC}$, point $E$ is the midpoint of $\overline {BC}$, point $H$ is the midpoint of $\overline {AF}$, and point $G$ is the midpoint of $\overline {BF}$.

Examine this carefully, find the similar triangles, and use their properties. Don't forget to look for congruent triangles as well.


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# Rusinkiewicz table BSDF¶

## Description¶

This BSDF model uses tabulated values. The coordinate system is the described in A new change of variables for efficient BRDF representation. The four geometric variables are thetaH, phiH, thetaD, phiD. This variable change is more efficient than the classical inbound/outbound vectors for all glossy materials.

The BSDF may be anisotropic if it depends on phiH.

This tabulated format is not currently editable in the graphical user interface, and should be provided in OCXML or OCBIN file formats.

The BSDF coefficient may be RGB, spectral values, or any set of channels having a primary spectrum. These primaries are represented by the spectrum children nodes. For instance:

• An achromatic (gray) BSDF will have a single spectrum child primary. The spectrum will be uniform, with a value of 1
• A RGB BSDF will have three primaries, each being set to R, G and B primary spectrum using preset spectra.
• A spectral BSDF will, for instance use a set of square spectra as primaries.

The grid on the H vector is defined as follows:

• thetaH takes a list of values, not necessarily evenly spaced. The first value is always 0° and the last 90°
• for each thetaH value, phiH can take a different number of evenly spaced values from 0° to 360°. This results in an igloo-shaped grid.
• A phi_h_sym parameter defines the symmetry along phiH

The symmetry parameter phi_h_sym is interpreted as follows:

• 0 or 1 means no symmetry, the first phiH is 0 and the last one is 360*(1-1/num_phi_out).
• -1 is an axial symmetry along the incident plane. The first phiH is 0 and the last one is 180.
• -2 is an axial symmetry plus a periodicity of 180°/2 = 90°. The first phiH is 0 and the last one is 90
• A value n above 1 means a periodicity of 360°/n. The first phiH is 0 and the last one is 360*(n-n/num_phi_out).

The grid on the D vector is defined the same way except:

• thetaD values are always evenly-spaced between 0° and 90°. The number of thetaD angles is then deduced from the number of values in the num_phi_d table
• there is no symmetry parameter for phiD is always 2 (which derives from the BRDF reciprocity)

Note

## Children Nodes¶

This node is a spectrum list. It may have a variable number of spectrum children.

 user-defined First primary user-defined Second primary user-defined ...

## Ocean XML 3.0 example¶

<bsdf type="rusinkiewicztable" name="brdf">
<spectrum type="uniform" name="" id="0" value="1"/>
<flist name="theta_h">0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90</flist>
<ilist name="num_phi_h">2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3</ilist>
<ilist name="num_phi_d">1 1 2 3 3</ilist>
<ilist name="phi_h_sym">-2</ilist>
<flist name="values">
11.55 13.4572 24.1996 0 81.4196 0 0 121.733 0 0
0 0 0 0 0 0 0 0 0 0
10.4874 12.1374 20.2484 19.8404 58.7873 81.79 59.5463 86.5922 81.79 90.79
9.71542 11.3007 19.3251 21.8282 61.1622 81.79 66.633 91.773 81.79 101.26
10.0996 11.7601 21.9836 18.4938 73.7751 0 20.19 111.247 0 0
10.0043 10.8436 17.8292 17.4581 50.8335 81.79 44.5635 75.6779 81.79 90.79
8.5122 9.47786 16.4763 19.6714 50.5041 81.79 58.5099 76.6955 81.79 89.0134
<!-- Actual data skipped -->
</flist>
</bsdf>

The BRDF values are then given in a single list , by order of :

1. thetaH
2. phiH


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# Year: 1998

### Photomodulated thermoreflectance detection of hydrogen gas using optically thin palladium film on silicon oxideKalli K, Othonos A, Christofides C, Spetz A, Lundstrom I

The sensitivity of various thicknesses of optically thin film palladium layers evaporated onto silicon oxide substrate is investigated in the presence of a hydrogen/air atmosphere at room temperature. The magnitude of the resulting reflectivity change is measured using an excite-probe technique, through laser excited photothermal modulation of a probe beam. This allows for the recovery of information from both the amplitude and phase channels of the hydrogen sensor output. Data indicates that concentrations of 0.1% hydrogen in the presence of a balanced air mixture and at room temperature may be measured with an 8 nm palladium film. The presence of inhomogeneities in the palladium layers leads to anomalous behavior

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### Temperature-induced reflectivity changes and activation of hydrogen sensitive optically thin palladium films on silicon oxideKalli K, Othonos A, Christofides C, Spetz AL, Lundstrom I

The optical properties of several thin metal film palladium-silicon oxide structures are examined at room temperature before and after annealing to 200 °C and also at 90 °C—in all cases in the presence of hydrogen gas. Multicycling sample activation is shown to occur in the presence of hydrogen at room temperature with an increase in reflectivity on exposure to hydrogen, in contrast to thicker 80 Å films. The reflectivity change increases with increasing film thickness (1–10 Å). The surface activation at room temperature, before and after annealing to 200 °C, is compared with the performance at 90 °C, where it is shown that heat treatment strongly influences the behavior of the metal film

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### Probing ultrafast carrier and phonon dynamics in semiconductorsOthonos A

Over the past 2 decades there has been tremendous advancements in the field of ultrafast carrier dynamics in semiconductors. The driving force behind this movement other than the basic fundamental interest is the direct application of semiconductor devices and the endless need for faster response and faster processing of information. To improve and develop microelectronics devices and address these needs, there must be a basic understanding of the various dynamical processes in the semiconductors which have to be studied in detail. Therefore, the excitation of semiconductors out of their equilibrium and the subsequent relaxation processes with various rates has become a key area of semiconductor research. With the development of lasers that can generate pulses as short as a few femtoseconds the excitation and subsequent probing of semiconductors on an ultrashort timescale have become routine. Processes such as carrier momentum randomization, carrier thermalization, and energy relaxation have been studied in detail using excite-and-probe novel techniques. This article reviews the status of ultrafast carrier and phonon dynamics in semiconductors. Experimental techniques such as excite-and-probe transmission, time-resolved up-conversion luminescence, and pump-probe Raman scattering along with some of the significant experimental findings from probing semiconductors are discussed. Finally, a selfconsistent theoretical model, which correlates the carrier and phonon dynamics in germanium on an ultrashort time scale, is described in detail.

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# Year: 1997

### Hydrogen gas detection via photothermal deflection measurementKalli K, Othonos A, Christofides C

A study of a thermal wave hydrogen sensor interrogated via transverse optical beam deflection spectroscopy is presented. The sensor is a thin film polyvinylidene fluoride film coated with a thin palladium layer. The sensitivity to hydrogen results from thermal boundary condition changes at the gas–film interface and depends upon the thermophysical properties of the gas. A simple one-dimensional model is developed to qualitatively and semi-quantitatively describe the experimental results and it shows good agreement with the experiment. Concentrations of 0.1% hydrogen in the presence of a balanced air mixture and at room temperature were measured for this sensor and they indicate possible sensitivities approaching 100 ppm.

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### Photothermal radiometric and spectroscopic measurements on silicon nitride thin filmsNestoros M, Gutierrez-Llorente A, Othonos A, Christofides C, Martinez-Duart JM

Thin films of silicon nitride of various thicknesses, deposited by radio frequency magnetron sputtering on silicon quartz substrate, have been characterized by laser-induced and frequency scanned photothermal radiometry. Fourier transform infrared spectroscopy was also used to provide a qualitative description of the behavior of the films in the infrared range which shows favourable properties of these coatings to be used in passive cooling applications.

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### Fiber Bragg gratingsOthonos A

Since the discovery of photosensitivity in optical fibers there has been great interest in the fabrication of Bragg gratings within the core of a fiber. The ability to inscribe intracore Bragg gratings in these photosensitive fibers has revolutionized the field of telecommunications and optical fiber based sensor technology. Over the last few years, the number of researchers investigating fundamental, as well as application aspects of these gratings has increased dramatically. This article reviews the technology of Bragg gratings in optical fibers. It introduces the phenomenon of photosensitivity in optical fibers, examines the properties of Bragg gratings, and presents some of the important developments in devices and applications. The most common fabrication techniques (interferometric, phase mask, and point by point) are examined in detail with reference to the advantages and the disadvantages in utilizing them for inscribing Bragg gratings. Reflectivity, bandwidth, temperature, and strain sensitivity of the Bragg reflectors are examined and novel and special Bragg grating structures such as chirped gratings, blazed gratings, phase-shifted gratings, and superimposed multiple gratings are discussed. A formalism for calculating the spectral response of Bragg grating structures is described. Finally, devices and applications for telecommunication and fiber-optic sensors are described, and the impact of this technology on the future of the above areas is discussed.

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### Laser photothermal diagnostics of genuine and counterfeit British and United States banknotesOthonos A, Mandelis A, Nestoros M, Christofides C

Laser-induced, frequency-scanned IR photothermal radiometry was used to investigate the thermophysical properties of the paper on which several genuine and counterfeit British (£10) and U.S. ($50,$100) currency bills were printed. The radiometric photothermal amplitudes and phases were further compared with a theoretical model, which yielded simultaneous quantitative measurements of the thermal diffusivities and conductivities of the bills. Both statistical and single-specimen results demonstrated the excellent thermophysical resolution of the technique with prospects for its use in the nonintrusive, on-line identification of counterfeit banknotes.

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### Diagnostics of nonradiative defects in the bulk and surface of Brewster-cut Ti:sapphire laser materials using photothermal radiometry Vanniasinkam J, Munidasa M, Othonos A, Kokta M, Mandelis A

The understanding of the problem of nonradiative energy conversion in solid-state laser materials is a key factor in improving the overall efficiency of solid-state lasers. Furthermore, the reduction of the heat generated in an optically pumped laser crystal can lead to several new applications of solid-state lasers, especially in the high-power region. To improve the quality of grown crystals, laser crystal growers require accurate techniques to perform the quality control that is so vital to improving the growth process. Using a time-domain approach and a time-domain theoretical treatment of the IR radiative emission signal, it was determined that one may probe nonradiative surface and bulk processes by monitoring different time ranges. Our results show that photothermal radiometry can be used as a single-ended technique to evaluate both the bulk and surface nonradiative energy conversion rates in a solid-state laser material. This technique was compared to the standard laser cavity technique and it was concluded that photothermal radiometry can provide additional information to the standard technique by identifying the sources of heat generation as either surface- or bulk-originating

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# Year: 1996

### Ultrafast dynamics of nonlinear absorption in low-temperature-grown GaAsBenjamin SD, Loka HS, Othonos A, Smith PW

We present the results of a study of the subpicosecond dynamic behavior of optically induced absorption changes in low‐temperature‐grown GaAs. We show that the observed behavior is dominated by mid‐gap trap states, and can be accurately modeled by the rate equations previously developed to describe quasi‐cw results. Our data give the first approximate values for trap emptying times in this material

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### Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysisLeBlanc M, Huang SY, Ohn M, Measures RM, Guemes A, Othonos A

A method of extracting the strain profile along a fiber Bragg grating from the intensity reflection spectrum is described. The procedure is based on a filter synthesis theory that relates the aperiodicity of a grating with its reflection spectrum. To illustrate the approach, we measured the strain profile near a hole in a plate and obtained a strain resolution of 80 {\textmu}$\epsilon$. The spatial resolution depends on the strain gradient; i.e., the higher the gradient, the better the resolution. A resolution of 0.8 mm was achieved for a 5-mm grating with a gradient of 250 {\textmu}$\epsilon$/mm.

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### Non-contacting measurements of photocarrier lifetimes in bulk- and polycrystalline thin-film Si photoconductive devices by photothermal radiometryMandelis A, Othonos A, Christofides C, Boussey-Said J

Laser‐induced and frequency‐scanned infrared photothermal radiometry was applied to a crystalline‐Si photoconductive device, and to polysilicon thin‐film photoconductors deposited on oxidized Si substrates by an LPCVD method. A detailed theoretical model for the radiometric signal was developed and used to measure the free photoexcited carrier plasma recombination lifetime, electronic diffusivity and surface recombination velocity of these devices, with the simultaneous measurement of the bulk thermal diffusivity. A trade‐off between detectivity/gain and frequency‐response bandwidth was found via the lifetime dependence on the wafer background temperature rise induced by Joule‐heating due to the applied bias. This effect was most serious with the bulk‐Si device, but was limited by the high resistivity of the LPCVD thin‐film devices. In the case of the bulk‐Si device, the results of photothermal radiometry were compared with, and corroborated by, frequency‐scanned photocurrent measurements. More sophisticated analysis was shown to be required for the interpretation of the polysilicon photoconductor frequency‐responses, perhaps involving the fractal nature of carrier transport in these grain‐structured devices.

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### Multi-wavelength Raman probing of phosphorus implanted silicon wafersOthonos A, Christofides C

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, DOI: 10.1016/0168-583X(96)00304-7Download
Raman spectroscopy is performed on phosphorus implanted silicon wafers with several excitation laser wavelengths ranging from 458 nm to 752.5 nm. The silicon layers were implanted with various implantation energies and doses, ranging below and over the critical dose of amorphization. A factor [kappa], relating the Raman intensity of the implanted samples with that of the pure crystalline silicon is introduced, and used to correlate the effects of ion implantation at different doses, different implantation energies and various annealing temperatures, on the silicon lattice.

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### Spectrally broadband Bragg grating mirror for an erbium-doped fiber laserOthonos A, Lee X, Tsai DP

The authors design and demonstrate a high-reflector broadband Bragg mirror for a fiber laser system. A T-matrix formalism was used to design a broadband intracore mirror consisting of a series of Bragg gratings. Ultraviolet light from a KrF excimer laser was used in an interferometric setup to inscribe these Bragg gratings in a photosensitive fiber. This resulted in a broadband Bragg mirror covering a wavelength range of approximately 3.5 nm. An all-Bragg grating, erbium-doped fiber laser cavity is demonstrated using this Bragg mirror as the high reflector and a single narrowband Bragg grating centered at 1550 nm as the output coupler. Tunability of the fiber laser was achieved over the range of the high reflector using strain-induced changes on the output coupler.

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### Photothermal radiometric investigation of implanted silicon: The influence of dose and thermal annealingOthonos A, Christofides C, Mandelis A

Photothermal radiometric measurements were performed on phosphorus implanted and annealed silicon wafers. Data were collected over modulation frequencies ranging between 0.1 and 100 kHz with the 488 nm Ar ion laser line as the excitation source. The sensitivity of this technique on implantation dose and annealing temperature is discussed. A semiquantitative analysis of the data is also carried out

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### Phase shifted Bragg gratings formed in optical fibres by post-fabrication thermal processingUttamchandani D, Othonos A

Fibre Bragg gratings have been post-fabrication processed using localised heat treatment, with significant changes to their transmission and reflection characteristics being observed. Experimental results of the spectral changes, together with an explanation of their origin, are provided in this article.

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# Year: 1995

### Photoluminescence measurements on phosphorus implanted silicon: Annealing kinetics of defectsOthonos A, Christofides C

Room‐temperature photoluminescence measurements are performed in order to study the effect of thermal annealing on phosphorus implanted silicon wafers. Measurements are carried out at near band gap excitation with a Nd:YAG laser operating at 1.06 μm. Photoluminescence measurements are also carried out with 0.488 μm laser excitation. It was found that implantation conditions (dose and energy) and annealing temperature strongly influence the intensity of the photoluminescence signal. Contribution from the bulk silicon and the effects from the ion implantation to the photoluminescence signal are discussed.

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### Novel and improved methods of writing Bragg gratings with phase masksOthonos A, Lee X

The authors demonstrate the importance of spatial coherence of the writing beam for inscribing Bragg gratings with a phase mask. Bragg gratings were written using a normal excimer laser with the fiber placed at various distances away from the phase mask. This was repeated with an excimer laser that was modified to improve the beam spatial coherence showing dramatic improvement in the ability to inscribe gratings. Tunability of the inscribed Bragg grating wavelength, utilizing a single phase mask in conjunction with the improved spatial coherence of the excitation source, is demonstrated

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### Narrow linewidth excimer laser for inscribing Bragg gratings in optical fibersOthonos A, Lee X

A spectrally narrow linewidth KrF excimer laser has been developed for the application of writing Bragg gratings in optical fibers. Two air spaced etalons 80 and 6 cm−1 have been incorporated within the laser cavity resulting in a laser line with a linewidth of approximately 4 pm. A stable wavelength setting for writing Bragg gratings has been achieved without the necessity of a feedback mechanism. A study of the formation of Bragg grating in optical fibers with this narrow linewidth KrF excimer laser has been carried out. High quality gratings have been demonstrated in hydrogen sensitized fibers with a pulse energy density as low as 20 mJ/cm2. Limitations and various problems encountered in inscribing Bragg gratings (such as two simultaneous grating lines) with the narrow linewidth excimer laser source are also discussed.

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### Determining erbium distribution in optical fibers using phase-sensitive confocal microscopyOthonos A, Wheeldon J, Hubert M

Confocal optical microscopy augmented by the phasesensitive detection technique has been used to determine the erbium ion distribution in the core of single-mode optical fibers. The fluorescence at 565 nm generated by erbium ions under 488 nm excitation has been used to map the distribution of these ions in several doped fibers and the total ion concentration was estimated. The minimum concentration of erbium ions that can be measured using this technique is estimated to be of the order of a part per million.

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### High-Resolution Quadrature Photopyroelectric Spectroscopy of a-Si:H Thin Films Deposited on Silicon WafersShen J, Mandelis A, Othonos A, Vanniasinkam J

The recently developed photothermal technique of quadrature photopyroelectric spectroscopy (Q-PPES) has been applied to measurements of amorphous Si thin films deposited on crystalline Si substrates. Direct, meaningful comparisons have been made between purely optical transmission in-phase (IP-PPES) spectra, and purely thermal-wave sub-gap spectra with the use of a novel noncontacting PPES instrument to record lock-in in-phase and quadrature spectra, respectively. FT-IR transmission spectra have also been obtained for a comparison with this IP-PPES optical method. The results of the present work showed that the FT-IR method performs the worst in terms of spectral resolution of thin films and sub-bandgap defect/impurity absorptions inherent in the Si wafer substrate. The optical IP-PPES channel, however, albeit more sensitive than the FT-IR technique, fails to resolve spectra from surface films thinner than 2100 Å, but is sensitive to sub-bandgap absorptions. The thermal-wave Q-PPES channel is capable of resolving thin-film spectra well below 500 Å thick and exhibits strong signal levels from the crystalline Si sub-bandgap absorptions. Depending on the surface thin-film orientation toward, or away from, the direction of the incident radiation, the estimated minimum mean film thickness resolvable spectroscopically by Q-PPES is either 40 Å or 100 Å, respectively.

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# Year: 1994

### Optical spectroscopy on implanted and annealed silicon wafers: Plasma resonance wavelengthChristofides C, Othonos A, Bisson M, Boussey-Said J

A study of the effects of annealing temperature on phosphorus‐implanted silicon films is carried out. Fourier transform infrared spectroscopy has been performed with two different instruments in the spectral ranges of 0.75–4 μm and 3–25 μm. In the first spectrum range special attention was given to the influence of implantation dose on reflectivity. The minimum reflectivity associated with plasma resonance has been fully employed for estimation of the electrical activation of implanted impurities. Other conclusions concerning the activation of free carriers (implanted impurities) with implantation dose and annealing temperature have been reached

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### Raman spectroscopy and spreading resistance analysis of phosphorus implanted and annealed siliconOthonos A, Christofides C, Boussey-Said J, Bisson M

Raman and electrical characterization measurements are performed in order to study the effects of thermal annealing on phosphorus implanted silicon wafers. The silicon layers were implanted for various implantation energies and doses, below, and over the critical dose of amorphization. The post‐implanted period was followed by thermal isochronal annealing at various temperatures. Special attention has been given to the amorphous/crystal transition occurring at various annealing temperatures. A bi layer model [R. Loudon, J. Phys. (Paris) 26, 677 (1965)] has been used for a quantitative determination of the annealing temperature at which a complete annihilation of implantation defects takes place. For this analysis, Raman spectra, resistivity depth profiles, as well as 1D‐SUPREM III simulation were used.

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### Determination of erbium distribution in optical fibers using confocal optical microscopyUttamchandani D, Othonos A, Alavie AT, Hubert M

Confocal fluorescence microscopy has been used to detect the 565 nm wavelength fluorescence generated from Er+3 ions present in erbium doped optical fibers, thereby enabling the concentration profile of these ions in the fiber core to be determined. The fluorescence intensity distribution also enables the total Er+3 ion concentration in the fibers to be estimated, and the estimated values are shown to be in good agreement with data supplied by the fiber manufacturers

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# Number theory statements

A list of the statements appearing in our posts about number theory follows.

Theorem N.1: Fundamental theory of arithmetic (not proved) Every integer number greater than 1 can be written as a product of prime numbers. Moreover such expression, called factorization or decomposition into prime factors, is unique apart from the order of the factors.
Theorem N.2: Infinity of primes The number of primes is infinite.
Property N.1: Overestimation of binomials For all $n > 0$ and for all $m$: $\binom{n}{m} \leq 2^{n-1}$
Property N.2: Underestimation of the central binomials of the Pascal’s triangle For all $n \geq 2$: $\binom{n}{\frac{n}{2}} \geq \frac{2^n}{n}$ if $n$ is even, and $\binom{n}{\left \lceil \frac{n}{2} \right \rceil} = \binom{n}{\left \lfloor \frac{n}{2} \right \rfloor} \geq \frac{2^n}{n}$ if $n$ is odd.
Property N.3: Underestimation of the central binomial of Pascal’s triangle, even $n$ For all even $n \geq 2$: $\binom{n}{\frac{n}{2}} \geq \sqrt{2^{n}}$
Proposition N.1: Majorization of the product of primes up to $x$ For all $x > 0$: $\theta^{\star}(x) = \prod_{1 \leq p \leq x} p \leq 2^{2(x-1)}$
Theorem N.3: Bertrand’s postulate For all $n > 0$, there exists a prime number between $n + 1$ and $2n$.
Lemma N.1: Factorization of the binomial $\binom{2n}{n}$ In the factorization of the binomial $\binom{2n}{n}$, for $n > 0$, a prime number $p$ cannot have an exponent greater than $\log_p 2n$.
Proposition N.2: Computation of $\psi^{\star}(x)$ For every integer $x > 0$: $\psi^{\star}(x) = \prod_{p \leq x} p^{\left \lfloor \log_p x \right \rfloor}$
Corollary of Proposition N.2: Overestimation of $\psi^{\star}(x)$ with $\pi(x)$ For every integer $x > 0$: $\psi^{\star}(x) \leq x^{\pi(x)}$
Proposition N.3: Underestimation of $\psi^{\star}(x)$ For every integer $x > 0$: $\psi^{\star}(x) \geq \sqrt[3]{2^x}$
Lemma N.2: Reformulation of $\psi^{\star}(x)$ (“calculation by rows”) For every integer $x > 0$: $\psi^{\star}(x) = \left(\prod_{p \leq x} p\right) \cdot \left(\prod_{p^2 \leq x} p\right) \cdot \dots \cdot \left(\prod_{p^R \leq x} p\right)$
Proposition N.4: Connection between $\psi^{\star}$ and $\theta^{\star}$ functions For every integer $x > 0$: $\psi^{\star}(x) = \theta^{\star}(x) \cdot \theta^{\star}(\sqrt{x}) \cdot \dots \cdot \theta^{\star}(\sqrt[R]{x})$, where $R := \left \lfloor \log_2 x \right \rfloor$.
Lemma N.3: Underestimation of $\theta^{\star}(x)$ through $\pi(x)$ For every real number $\delta \geq 0$ and for every $x \gt 1$: $\theta^{\star}(x) \gt \left(x^{\delta}\right)^{\pi(x) - x^{\delta}}$.
Theorem N.4: Asymptotic equivalence and order of magnitude of $\theta(x)$ and $\psi(x)$ The functions $\theta(x)$ and $\psi(x)$ are asymptotically equivalent and have order $x$: $\theta(x) \sim \psi(x)$, $\theta(x) \asymp x \asymp \psi(x)$.
Theorem N.5: Asymptotical equivalence between $\pi(x)$ and $\frac{\theta(x)}{\log x}$ $\pi(x) \sim \frac{\theta(x)}{\log x}$
Corollary of Theorem N.5: Asymptotical equivalence between $\pi(x)$ and $\frac{\psi(x)}{\log x}$ $\pi(x) \sim \frac{\psi(x)}{\log x}$
Corollary II of Theorem N.5: Chebyshev’s Theorem: order of magnitude of $\pi(x)$ $\pi(x) \asymp \frac{x}{\log x}$
Lemma N.4: Lemma of bar chart area Let $c_1, c_2, \dots, c_n$ be natural numbers, with $n > 0$. Let $f: \{1, 2, ..., n\} \rightarrow \mathbb{R}$ be a function. Then the area $A$ of the bar chart made up of $n$ rectangles, each having basis $c_i$ and height $f(i)$, given by $A = c_1 f(1) + c_2 f(2) + \ldots + c_n f(n) = \sum_{i=1}^{n} c_i f(i)$, can also be computed with the formula \begin{aligned}A &= C_n f(n) + C_{n-1} (f(n-1) - f(n)) + \ldots + C_1 (f(1) - f(2)) \\&= \sum_{k = 1}^{n-1} C_k (f(k) - f(k + 1)) + C_n f(n)\end{aligned} where $C_k := c_1 + c_2 + \ldots + c_k = \sum_{i=1}^{k} c_i$.
Lemma N.5: Lemma of bar chart area, second form Let $c_1, c_2, \dots, c_n$ be natural numbers, with $n > 0$. Let $f: \{1, 2, ..., n\} \rightarrow \mathbb{R}$ be a function, and $\widetilde{f}$ a $C^1$ extension of $f$. Then the area $A$ of the bar chart made up of $n$ rectangles, each with basis $c_i$ and height $f(i)$, given by $A = c_1 f(1) + c_2 f(2) + \ldots + c_n f(n) = \sum_{i=1}^{n} c_i f(i)$, can be also computed with the formula $$C(n) f(n) - \int_1^n \overline{C}(k) \widetilde{f}'(t) dt$$ where $C: \{1, 2, ..., n\} \rightarrow \mathbb{N}$ is the function defined by $C(k) := c_1 + c_2 + \ldots + c_k = \sum_{i=1}^{k} c_i$.
Theorem N.6: Approximation of the sum of inverses of the first positive integers

For all integers $n \gt 0$:

$$\sum_{k = 1}^n \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} \approx \log n + \gamma$$

where logarithm base is Napier’s number $e$, while $\gamma \approx 0.58$ is the Euler’s constant. In particular:

$$\sum_{k = 1}^n \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} = \log n + \gamma + O\left(\frac{1}{n}\right)$$
Property N.4: Upper and lower bounds for the value assumed by a function defined on integer numbers, by means of integrals of an extension

Let $f: I \rightarrow \mathbb{R}$ be a function defined on a set $I \subset \mathbb{Z}$.
Let $\overset{\sim}{f}: \overline{I} \rightarrow \mathbb{R}$ an extension of $f$, where $\overline{I} := \bigcup_{n \in I} [n, n + 1)$. Then:

• If $\overset{\sim}{f}$ is increasing, then $f(n) \leq \int_n^{n+1} \overset{\sim}{f}(t) dt$
• If $\overset{\sim}{f}$ is decreasing, then $f(n) \geq \int_n^{n+1} \overset{\sim}{f}(t) dt$

Let $\underset{\sim}{f}: \underline{I} \rightarrow \mathbb{R}$ be an extension of $f$, where $\underline{I} := \bigcup_{n \in I} (n - 1, n]$. Then:

• If $\underset{\sim}{f}$ is increasing, then $\int_{n-1}^n \underset{\sim}{f}(t) dt \leq f(n)$
• If $\underset{\sim}{f}$ is decreasing, then $\int_{n-1}^n \underset{\sim}{f}(t) dt \geq f(n)$
Lemma N.6: Order of magnitude of the sum of a fraction logarithms when the denominator changes $$\sum_{n=1}^x \log \left(\frac{x}{n} \right) = O(x)$$.


text: It is a class of model that captures a suite of different standard temporal structures in time series data. 2 Basic options in EViews 1 1. I have time series which is stationary and I am trying to predict n period ahead value. log prices and output) so we consider the rst di erence to reach stationarity. Incidentally, though a SVAR model is a structural model, it departs from a reduced form VAR(p) model and only restrictions for Aand Bcan be added. - VARs can be used to quantitatively construct a particular model • Question that can (in principle) be addressed by VAR: - 'How does the economy respond to a particular shock?How does the economy respond to a particular shock?' - Answer can be very useful: • for discriminating between models. Session 3: Structural VAR using Eviews Types of VAR : Reduced Form (approximate) and Structural Form (based on theory) This technique is strongly based on theoretical relationship between the variables. And, if the model’s parameters were unstable over the sample period, then model was not even a good representation of how the series evolved over the sample period. Structural VAR representation Suppose we have the following bivariate VAR(1) model of the following form (Note: we suppress the intercept term for simplicity): In the framework, y and x are specified to be related contemporaneously as well as with lags and u1t and u2t are structural shocks of yt and xt. VAR in EViews. called upon to determine how much one variable will change in response to a change in some other variable. Modelling in Eviews •In Eviews for the model to have a unique solution, there should typically be as many equations as there are endogenous variables •Each equatin in the model must have a unique endogenous variable assigned to it. • VAR/Eviews. (VAR) Model? Question. ARIMA is an acronym that stands for AutoRegressive Integrated Moving Average. Ouliaris1, A. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. @TREND(d) time trend variable normalized to be zero in period d, where d is a date or observation number If the data are quarterly, a useful way to define a trend is t = 1946 + @TREND(1946. For the garch(1,1) model the key statistic is the sum of the two main parameters (alpha1 and beta1, in the notation we are using here). Sebelum melakukan pengujian regresi data panel, ada baiknya kita mengenal 3 pendekatan yang digunakan dalam metode analisis regresi data panel, ketiga model itu ialah common effect, fixed effect dan random effect dan berikut penjelalasan ringkas mengenai ketiga model tersebut:. 1 Basic descriptive statistical summary 7 1. VAR Specification에서 Rank를 1로 설정했기 때문에 하나만 나오는 것이지요. Introduction to ARCH & GARCH models Recent developments in ﬁnancial econometrics suggest the use of nonlinear time series structures to model the attitude of investors toward risk and ex-pected return. The forecasts are evaluated using the Kupiec test with a five percent significance level. 1: VAR Estimation and Variance Decomposition. reg lwage exper tenure educ if female==1. The key is that for annual countries, certain variables are defined as averages of future quarterly variables (BEPMP, BEX00$, BEPW$,. See the READ_ME text object in the EViews workfile for more details. • VAR/Eviews. Multivariate Regression Analysis | Stata Data Analysis Examples Version info: Code for this page was tested in Stata 12. The line chart shows how a variable changes over time; it can be used to inspect the characteristics of the data, in particular, to see whether a trend exists. Actually, when an LES model is fitted to the same data, the optimal value of alpha turns out to be around 0. The GVAR Toolbox was originally launched in December 2010 with the release of version 1. Estimation of Cointegrated VAR Models. 44 answers. Time Series and Forecasting A time series is a sequence of observations of a random variable. We will then dig deeper and calculate incremental value at risk, marginal value at risk and conditional value at risk. Tramo/Seats X-11 seasonal adjustment, solving model objects with more than 10 equations, storing EViews objects to databases, database autosearch, and redirection of print output to text or RTF files. -Cholesky (with and without degree of freedom adjustment for small sample correction). The model is particularly useful for nowcasting. This instance can be better analysed in the context of a vector-error-correction model (VECM). EViews available as stand-alone to students in the Ba2 and Ba3 phase Download Free eView, eView 1. See the READ_ME text object in the EViews workfile for more details. • Any variable that is not assigned as an endogenous variable is considered exogenous to the model. • EViews generates a lot of information that you will not use for your analysis. Generally, for m number of observations, we could have m-1 number of cointegration vectors. Untuk uji chow tidak mungkin hasilnya random, karena uji chow sendiri adalah uji untuk menentukan apakah model yang tepat Common effect atau fixed effect. Clearly, this is now a three-variable OLS model. There are causal and statistical interpretations of exogeneity. So of course i estimated the VAR with 1998-1 - 2006-4, and then did step by step of the above answer, but the problem is that eviews seems to change the data from previous years (i. Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. · Use Eviews to conduct vector autoregressive (VAR) model, Granger causality tests, impulse response function and variance decomposition method. In today’s VaR Excel spreadsheet walk through session we will do just that. *** If you have any query please email me "[email protected] You may obtain the ASURITE ID at Computer Commons computing sites (see the support staff for assistance). For a simulation under VAR expectations, the ld_some_eqs add-in loads a subset of FRB/US. The line chart shows how a variable changes over time; it can be used to inspect the characteristics of the data, in particular, to see whether a trend exists. It will produce unbiased estimates of the coefficients, use all the data available, and produce the smallest standard errors. Estimating Vector Autoregression Model with The U. 1)/4 This is a variable that increments one each year (. The coefficients in a linear-log model represent the estimated unit change in your dependent variable for a percentage change in your independent variable. Final part of the training describes ways to model volatility of time series in form of Autoregressive Conditional Heteroscedasticity-models (ARCH, GARCH). That is, can we assume a long run relationship in the model despite the fact that the series are drifting apart or trending either upward or downward?. Oleh karena dari hasil uji stasioneritas/uji unit root, kita mendapatkan bahwa ada sebuah variabel yang stasioner pada level sedangkan dua variabel lainnya stasioner pada differens pertama maka kita akan mengajukan model analisis VAR dalam differens (VAR in difference). The figure below is the standard output view of ARDL estimated for two variables. Subscribe for more vide. Also, if you want to save the standard errors, enter a name in the “S. It is a one-period shock which reverts to zero immediately. Cara Membaca Hasil Regresi Data Panel Model Random Effect Model Random Effect. Also I basically get the same result from the model estimation "model1" to Eviews. 1 Stationarity and unit root testing 353 8. Watch in our app. 2-2 JesperHybelPedersen 11. Model umum, VAR dengan lag 1: Kelebihan dari model VAR adalah: 1. Stationarity. Seemingly Unrelated Regression Equations Models. In its reduced form, the right-hand side of each. 다만, 요한슨 공적분 검정에서 나오지 않았던 상수항이 나오네요. 315) remarked that “a major contribution of the ARCH literature is the ﬁnding that apparent. The @log function in Eviews can be performed on either your independent or dependent variable. Model ekonometrika yang dibangun berdasarkan hubungan antar variabel yang mengacu pada model dan digunakan untuk melihat hubungan kausalitas antar variabel. Time Series Analysis III. A Guide to Basic Programming for Simulation with EViews* (Version 4. Johansen Cointegration Test with EViews In the previous discussion we had shown that how we do the cointegration test what we called it as Engle and Granger tes t. • Example 2: For the binary variable, in/out of the labor force, y* is the propensity to be in the labor force. Finally, the existence of any type of learning dynamics by private agents or the monetary authorities deﬁnitely favors a model with smooth and continuous drifting coeﬃcients over a model with discrete breaks. The data are found in the appendix to Lütkepohl (1993). log prices and output) so we consider the rst di erence to reach stationarity. A VAR that does allow for contemporanous relationships among its variables may be written as \begin{align}. Increasingly however, econometricians are being asked to forecast and analyze the size of the errors of the model. There are several ways to estimate VAR model in EViews. , R 2 , F-statistic, D-W statistic) are identical across the outputs. ahead=15, runs=100)" gives me very different views to Eviews, and I'm still searching on whether this command uses cholesky decomposition and one SD shock. In statistics, econometrics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. I decided to try the model and used this article by BoE as a guide (starting from page 14):. errors for each of the dependent variables. LeSage's Econometric Toolbox to compute p-values from the normal, F, and chi-square distributions. ARIMA is an acronym that stands for AutoRegressive Integrated Moving Average. Nah seandainya hasil dari pengujian itu menunjukan model common effect, maka dilanjutkan ke pengujian selanjutnya, yaitu uji LM test. Assume that all variables are endogenous in the model and no need to choose any variables for normalization. As far as I understand it, the concept relates to the problem of recovering the true $\epsilon$ of the underlying structural equations. This approach must be used when making changes to functional forms in EViews 7 and may be optionally used for this purpose in EViews 8. In response to exogenous growth in productivity and population, the neoclassical growth model predicts that output, consumption and investment will grow in a balanced. Jadi, karena alasan itu sob, perlu diadakan uji stasioneritas variabel pada data panel (panel unit root test). Quantitative Macroeconomic Modeling with Structural Vector Autoregressions { An EViews Implementation S. Of course, if there is a reaction of one variable to an impulse in another variable. TIME SERIES ECONOMETRICS STRUCTURAL VAR: THE AB MODEL 2. See end of article for workings of the reduced form model Note: The Reduced form model determines the total effect, direct effect and indirect effect of a change in the predetermined variables on the dependent variables, after. Asymmetric Co-integration using Eviews TIME SERIES ECONOMETRICS WORKSHOP: "Asymmetric Co-integration, NARDL and Structural VAR" by Professor Mansor Ibrahim Markov-Switching using R. I have no trouble adding ARMA components, dummy variables, trend, etc. 0: An Overview Some Preliminaries In what follows it will be useful to distinguish between ex post and ex ante forecasting. If the equations to be estimated is: Y i = $0 +$1X i + ,i Enter in the box, Y C X where C indicates to EViews to include a regression constant. However, what if you want specific lags only? For example, what if I wanted lags 1, 2, and 4 only in a VAR? Inputting P=4 in VAR will give me lags 1,2,3 and 4, but I would like to exclude the third lag. Vector Autoregressions • VAR: Vector AutoRegression - Nothing to do with VaR: Value at Risk (finance) • Multivariate autoregression • Multiple equation model for joint determination of two or more variables • One of the most commonly used models for applied macroeconometric analysis and. The default is lags(1 2). AHN 1 INSTRUCTION FOR ACCESSING AN INSTRUCTOR VOLUME Special Note: To use the computers located at ASU, you must have an ASURITE ID. Please Note: The purpose of this page is to show how to use various data analysis commands. In its reduced form, the right-hand side of each. Here students learn about Durbin Watson, residual diagnostic, DW analysis, OLS equation and estimation, Gold and BSE index examples, DW calculated, multi-asset analysis, Breusch Godfrey test, LM test etc. 1 ¹ 0 provides a test of the hypothesis that Y. In this case, the questions are about volatility, and the standard tools have become the ARCH/ GARCH models. Various alternative multiple regressions models are presented based on a single time series, bivariate, and triple time-series, which are developed by taking into account specific growth patterns of each dependent variables, starting with the simplest model up to the most advanced model. EViews solves for the endogenous variables, given data for the exogenous variables. As the author of the original post here I struggle to handle thw Warning of Singular Covariance Matrix I have daily consumer expenses data for a period of 2 years. Estimating Vector Autoregression Model with The U. calling syntax of VAR is a bit complicated because it is designed to handle multivariate data in matrices, data frames as well as "timeSeries"objects. Andrew Patton's Matlab code page. The first one is through the main menu. A Short Introduction to Eviews 3 4 Importing data into Eviews The are two ways to get your dataset into Eviews. Contents of the EViews equation window 3. Forecasting Using Eviews 2. Properties and Estimation of GARCH(1,1) Model Petra Posedel1 Abstract We study in depth the properties of the GARCH(1,1) model and the assump-tions on the parameter space under which the process is stationary. VAR model-the impact of a macroeconomic policy on inﬂation and economic activity Katarzyna Lada, Piotr Wójcik 22. Model umum, VAR dengan lag 1: Kelebihan dari model VAR adalah: 1. • Standard information to report on a regression table o Dependent variable o Explanatory variables. Also I basically get the same result from the model estimation "model1" to Eviews. Again, The basic are very simple and intuitive. A useful generalization of this model is the GARCH parameterization introduced by Bollerslev(1986). The key is that for annual countries, certain variables are defined as averages of future quarterly variables (BEPMP, BEX00$, BEPW$,. Markov-Switching vector autogressive model (MS-VAR) means an expert for Markov-Switching vector autogressive models, but this example might help getting you. In EViews, the model object combines such equations into a single entity that may be used to create a joint forecast or a simulation of all endogenous variables of the model. Multivariate Regression Analysis | Stata Data Analysis Examples Version info: Code for this page was tested in Stata 12. If you are after the theory of VARs you may want to look at these clips VAR Setup. • The residuals from the regression we just ran are automatically stored by EViews as the variable resid. Vector-Autoregressive (VAR) and Vector-Error-Correction-Models (VEC) are part of the training as a special case of systems of equations. Here also. DATA ANALYSIS NOTES: LINKS AND GENERAL GUIDELINES. Latent Variable Formulation For the rest of the lecture we'll talk in terms of probits, but everything holds for logits too One way to state what's going on is to assume that there is a latent variable Y* such that Y* =Xβ+ε, ε~ N(0,σ2) Normal = Probit. log prices and output) so we consider the rst di erence to reach stationarity. Johansen Cointegration Test with EViews In the previous discussion we had shown that how we do the cointegration test what we called it as Engle and Granger tes t. However, when checking for residual autocorrelation the null hypothesis of no autocorrelation is rejected for a high number of lags. The default is lags(1 2). Contents of the EViews equation window 3. Stationarity. 1 EViews workfile and descriptive data analysis 1 1. " The above window is achieved, by first pressing variable sp05, then holding ctrl and press sp06 and so forth. Also, if you want to save the standard errors, enter a name in the “S. Federal Funds Rate, Nominal Interest Rate, Exchange Rate and Industrial Production as Endogenous Variables. A popular and widely used statistical method for time series forecasting is the ARIMA model. ARDL with Cointegrating Bounds using EVIEWS 9 Posted on May 2, 2015 October 17, 2015 by Noman Arshed Posted in Nomi's Blog Tagged ARDL model , Eviews Well we can now have ARDL module in EViews 9 which can replicate same results as compared to what Microfit can do with the advantage that we can have more than two lags and more than 6 variables. The log of the quantity of beef demanded is the dependent variable; the logs of. It is a class of model that captures a suite of different standard temporal structures in time series data. Better estimates and it is possible to check for model stability and check forecasting ability of model by withholding data. future values of each of the variables to a one-unit increase in the current value of one of the VAR errors. I have no trouble adding ARMA components, dummy variables, trend, etc. For information on estimating models, see VAR Model Estimation. How to Use EViews (Econometric Views) EViews is a simple but flexible econometric software package that runs on both Windows m a-chines and Macintoshes. When is an Autoregressive Model Dynamically Stable? the EViews file that I used to create these data and charts is on the code I run a VAR model in STATA, and. We will then dig deeper and calculate incremental value at risk, marginal value at risk and conditional value at risk. 17 An example of the use of VAR models: the interaction between property returns and the macroeconomy 343 6. Interpreting Eviews Output. variables are uncorrelated with the explanatory variables that are in the model - then a random effects model is probably best. Please Note: The purpose of this page is to show how to use various data analysis commands. We will compare VaR results across SMA VaR, EWMA VaR, Variance co Variance VCV VaR, Historical Simulation VaR and Monte Carlo Simulation VaR. Introduction into Panel Data Regression Using Eviews and stata Hamrit mouhcene University of khenchela Algeria [email protected] You will note that we have both entered C as an exogenous variable, and checked the box instructing EViews to include a constant in the VAR. The @log function in Eviews can be performed on either your independent or dependent variable. In EViews, the model object combines such equations into a single entity that may be used to create a joint forecast or a simulation of all endogenous variables of the model. Two empirical applications forecasting Brazilian in⁄ation and U. juni2013 1 Introduction If we want to know how well our model does VaR calculation we would. But many (most?) time-series variables are nonstationary. NOTE: The programs for simulating the FRB/US model are written for use with the software EViews, available at www. Markov-Switching vector autogressive model (MS-VAR) means an expert for Markov-Switching vector autogressive models, but this example might help getting you. However, in an ex post forecast observations on both endogenous. Oleh karena dari hasil uji stasioneritas/uji unit root, kita mendapatkan bahwa ada sebuah variabel yang stasioner pada level sedangkan dua variabel lainnya stasioner pada differens pertama maka kita akan mengajukan model analisis VAR dalam differens (VAR in difference). The first four are suggested by the standard neoclassical growth model. They are circulated in order to help AGRODEP members address technical issues in their use of models and data. Johnson∗ University of San Diego Introduction In the Introduction: 1. FE explore the relationship between predictor and outcome variables within an entity (country, person, company, etc. Here students learn about Durbin Watson, residual diagnostic, DW analysis, OLS equation and estimation, Gold and BSE index examples, DW calculated, multi-asset analysis, Breusch Godfrey test, LM test etc. Note, specifically, that the license terms do not allow two users to share copies of the same license of EViews residing on two machines. The vector autoregressive (VAR) model is a general framework used to describe the dynamic interrelationship among stationary variables. Multiple Linear Regression Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Applications of regression analysis exist in almost every field. Since that time the VAR approach has been widely used in applied work. You may then use irf graph, irf table or other irf analysis commands to examine results. VAR models in which the lag length potentially differs across the variables in the model but is the same for a particular variable in each equation of the model. The included models are the Autoregressive Integrated Moving Average (ARIMA) model, the Vector Autoregression (VAR) model and the First-order Autoregression (AR(1)) model. EVIEWS TUTORIAL BY DR. However Gretl has the ability to use scripts R, Octave, Python etc. For information on creating VAR models, see Multivariate Time Series Model Creation. The persistence of a garch model has to do with how fast large volatilities decay after a shock. Section 12 Time Series Regression with Non-Stationary Variables The TSMR assumptions include, critically, the assumption that the variables in a regression are stationary. 44 answers. some or all variables in the VAR(p)-process are integrated of order one, i. Subscribe for more vide EView s Tutorial: Episode 1 - Inputting da ta from Excel. You may have noticed conflicting advice about whether to leave insignificant effects in a model or take them out in order to simplify the model. Although this method helps us to understand the basic principle of simulation and its operation, it might be tedious and time-consuming work because there are lots of repetitive steps. [email protected] • Standard information to report on a regression table o Dependent variable o Explanatory variables. The reader is referred to the monography. 1, and figures 3. com phone +213778080398 Panel data is a model which comprises variables that vary across time and cross section, in this paper we will describe the techniques used with this model including a pooled regression, a fixed. Economic theory often links variables contemporaneously, and if we wish to use the VAR to test those theories, it must be modified to allow for contemporanous relationships among the model variables. Structural VAR: the AB model 1. Again, The basic are very simple and intuitive. DATA ANALYSIS NOTES: LINKS AND GENERAL GUIDELINES. BEHAVIORAL MODELS The original meaning of a "structural" model in econometrics is explained in an article by Hurwicz (1962). In this example, a VAR model is estimated and forecast. autoregressive (VAR) models. Note:**** The views expressed in this site are those of my own and do not necessarily represent those of my employer. The log of the quantity of beef demanded is the dependent variable; the logs of. Incidentally, though a SVAR model is a structural model, it departs from a reduced form VAR(p) model and only restrictions for Aand Bcan be added. We will compare VaR results across SMA VaR, EWMA VaR, Variance co Variance VCV VaR, Historical Simulation VaR and Monte Carlo Simulation VaR. There are several ways to estimate VAR model in EViews. Pankratz (1991) refers to the ARIMAX model as dynamic regression. You do not always know the offset c, trend coefficient δ, coefficient β, autoregressive matrices Φ i, and moving average matrices Θ j. juni2013 1 Introduction If we want to know how well our model does VaR calculation we would. The new engine offers two new major priors; the Independent Normal-Wishart and the Giannone, Lenza and Primiceri, that compliment the previously implemented Minnesota/Litterman, Normal-Flat, Normal-Wishart and Sims-Zha priors. As the name implies, multivariate regression is a technique that estimates a single regression model with more than one outcome variable. (VAR) Model? Question. Coefﬁcients are extracted from a VECM in package tsDyn, or from a VECM obtained in package urca from ca. Introduction into Panel Data Regression Using Eviews and stata Hamrit mouhcene University of khenchela Algeria [email protected] For more information, see[TS] var intro. The associated parameters of the regression model will be interpreted and tested for significance and test the goodness of fit of the given regression model Requirements Detailed in course description below, prior knowledge of Quantitative Methods AND Econometrics techniques, MS Office and Paint is desired. 1 Basic descriptive statistical summary 7 1. You should confirm that these values are within the ranges you expect. Contents of the EViews equation window 3. How can we estimate the structural VAR in eviews. However, in an ex post forecast observations on both endogenous. 17 An example of the use of VAR models: the interaction between property returns and the macroeconomy 343 6. AGRODEP Technical Notes are designed to document state-of-the-art tools and methods. Here is a model comparison report that shows the results of fitting the ARIMA(2,1,0) model with constant, the ARIMA(0,2,1) model without constant, and the LES model:. wf1, contains data for the variables y1, y2, x1 and x2. There are several ways to estimate VAR model in EViews. p-value Most econometric packages provide the p-value (for a TWO-sided test), or probability (in EViews), for each and every test. Stationarity and nonstationarity estingT for integration Cointegration Error correction model Augmented D-F speci cation ADF how many lags? in general: the purpose is. (VAR) Model? Question. 6, because that cannot happen. You may then use irf graph, irf table or other irf analysis commands to examine results. Eviews specification-Residual: ignores the correlations in the VAR residuals; gives the MA coefficients of the infinite MA representation of the VAR. Subscribe for more vide EView s Tutorial: Episode 1 - Inputting da ta from Excel. This model is a totally general VAR-model - only the data vectors has been partitioned in 3 subvectors - the yt and the xt vectors between which we will test for causality and the zt vector (which may be empty) which we condition on. Cara estimasi model VAR sangat mudah yaitu dengan menggunakan OLS pada setiap persamaan secara terpisah. Assume our model has the following form: where signals 2 different states. It is used when there is no cointegration among the variables and it is estimated using time series that have been transformed to their stationary values. The Causal Structure of the Vector Autoregression in Economics - Kevin Hoover - Duration: 40:19. ) 52 The highest correlation is between the price of cars and the general price level. Hence, it is a stochastic process. Interpreting Eviews Output. A Short Introduction to Eviews 3 4 Importing data into Eviews The are two ways to get your dataset into Eviews. Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series. The resulting model is then estimated, and used to test the empirical relevance of the theory. Dependent variables in models are not only impacted by quantitative variables, but also are impacted by qualitative variables such as religions, gender, color, and geography. VAR in EViews. Chapter 2: Ordinary Least Squares In this chapter: 1. A univariate autoregression is a single-equation, single-variable linear model in which the cur- rent value of a variable is explained by its own lagged values. Once you have the time series data for these variables you need to upload them into Eviews and follow these steps:. txt) or view presentation slides online. Here, the model will again leave the constant unrestricted, corresponding to the DGP and Regression Model specified in Case 3 in Part 1 and Part 2. Model ekonometrika yang dibangun berdasarkan hubungan antar variabel yang mengacu pada model dan digunakan untuk melihat hubungan kausalitas antar variabel. Every value of the independent variable x is associated with a value of the dependent variable y. ARDL with Cointegrating Bounds using EVIEWS 9 Posted on May 2, 2015 October 17, 2015 by Noman Arshed Posted in Nomi's Blog Tagged ARDL model , Eviews Well we can now have ARDL module in EViews 9 which can replicate same results as compared to what Microfit can do with the advantage that we can have more than two lags and more than 6 variables. He demonstrated that this pattern of asymmetry can be derived from a structural representation of the VAR model that has asymmetric lags. For information on estimating models, see VAR Model Estimation. The equation C = 100 +. Vector-Autoregressive (VAR) and Vector-Error-Correction-Models (VEC) are part of the training as a special case of systems of equations. Thus y is CI(2,1), the variables in the VAR are all I(1) but the inference procedures are nonstandard. A time-series model can have heteroscedasticity if the dependent variable changes significantly from the beginning to the end of the series. Second, we study the six lag order selection criteria that are most widely used in the applied VAR literature: the LR, SLR and LM test and the AIC, HQC. In its reduced form, the right-hand side of each. A univariate autoregression is a single-equation, single-variable linear model in which the current value of a variable is explained by its own lagged values. [email protected] Pankratz (1991) refers to the ARIMAX model as dynamic regression. For example, there was a structural change in U. These make more sense in the context of a model with uncor-related errors across equations. you set to estimate VAR model in EVIEWS or STATA, results will be always same. Aim to promote the awareness of GVAR models and provide a platform for people to download the GVAR toolbox to help solving the GVAR models. However, we cannot be running the unrestricted VAR model using different lag lengths before deciding on the best model to adopt, there is a simplified way of obtaining the optimal lag structure at once given a variety of information criteria. Example 1: VAR model. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. Model VAR adalah model yang sederhana dan tidak erlu membedakan mana variabel yang endogen dan eksogen. The first volume of the EViews 7 User's Guide describes the basics of using EViews and describes a number of tools for basic statistical analysis using series and group objects. More likely, however, is that omitted variables will produce at least some. Data from five counties were chosen for. Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series. 1: VAR Estimation and Variance Decomposition. 1 Work les in EViews EViews design allows you to work with various types of data in an intuitive and convenient way. For more information, see[TS] var intro. In his current role, Azfar Hussain is part of the model risk management team at Discover Financial Services as a Senior Model Validation Specialist, performing model validation and risk management. So of course i estimated the VAR with 1998-1 - 2006-4, and then did step by step of the above answer, but the problem is that eviews seems to change the data from previous years (i. To estimate a time series regression model, a trend must be estimated. Multiple Linear Regression Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. 1 quarterly data of 1970q1 to 1991q4. Each entity has its own individual characteristics that may or may not influence the predictor variables (for example, being a male or female. Sometimes in time series work it is necessary to compute a new variable using data from several time periods, such as a growth rate. Vector Autoregressions • VAR: Vector AutoRegression - Nothing to do with VaR: Value at Risk (finance) • Multivariate autoregression • Multiple equation model for joint determination of two or more variables • One of the most commonly used models for applied macroeconometric analysis and. To accomplish this task, we first need to specify and estimate a model. One would like to investigate the impulse response relationship between two variables in a higher dimensional system. EViews 11 introduces a completely new Bayesian VAR engine that replaces one from previous versions of EViews. you set to estimate VAR model in EVIEWS or STATA, results will be always same. Please note that in EViews, the procedure is simply to run an initial VAR on the variables at level with the default settings and obtain the results. As the name implies, multivariate regression is a technique that estimates a single regression model with more than one outcome variable. Importing data from a spreadsheet file named Beef 2. It should be noted that the reduced form residuals. errors for each of the dependent variables. EViews help 3. Sayed Hossain welcomes you to Hossain Academy. It is primarily designed to work with time series data, 1 but can also be used for cross-section and panel data. Model VAR adalah model yang sederhana dan tidak erlu membedakan mana variabel yang endogen dan eksogen. Stationarity and nonstationarity estingT for integration Cointegration Error correction model Augmented D-F speci cation ADF how many lags? in general: the purpose is. The persistence of a garch model has to do with how fast large volatilities decay after a shock. You can trace this through the VAR model and see if it impacts the other variables in a statistically significant way. Section III illustrates the simulation study of the TVP regression model focusing on stochastic volatility. UNIT ROOT TESTS, COINTEGRATION, ECM, VECM, AND CAUSALITY MODELS Compiled by Phung Thanh Binh1 (SG - 30/11/2013) "EFA is destroying the brains of current generation's researchers in this country. To focus strictly on the mechanics at this point, however, these model-selection issues are postponed to a later section. Many of these relate to the Eviews interface, data handling, and graphs and tables. Modified Value at Risk (or MVaR) calculation, however, adjusts the standard deviation to account for skew and kurtosis in the returns distribution (greater negative skew and kurtosis act to increase VaR). The p-value tells us the lowest level of significance at which the null-hypothesis could be rejected. Vector Autoregressions • VAR: Vector AutoRegression - Nothing to do with VaR: Value at Risk (finance) • Multivariate autoregression • Multiple equation model for joint determination of two or more variables • One of the most commonly used models for applied macroeconometric analysis and. The Quadratic GARCH (QGARCH) model by Sentana (1995) is used to model asymmetric effects of positive and negative shocks. 44 answers. Learn what value at risk is, what it indicates about a portfolio, and how to calculate the value at risk (VaR) of a portfolio using Microsoft Excel. After the model has been ﬁtted to both variables, we can calculate the prediction errors. Unlike the single-equation model in which a dependent (y) variable is a function of independent (x) variables, other y variables are among the independent variables in each SEM equation. Note: The names of the variables must be legal in EViews (no more than 16 characters ; no spaces). Introduction to EViews 6. 1)/4 This is a variable that increments one each year (. " The above window is achieved, by first pressing variable sp05, then holding ctrl and press sp06 and so forth. You will note that we have both entered C as an exogenous variable, and checked the box instructing EViews to include a constant in the VAR. Even if we drop these variables one-by-one from the model, still we have a multicollinearity problem. There are several ways to estimate VAR model in EViews. Here students learn about Durbin Watson, residual diagnostic, DW analysis, OLS equation and estimation, Gold and BSE index examples, DW calculated, multi-asset analysis, Breusch Godfrey test, LM test etc. 1) In the previous section, using a 'step-by-step method', we learned how to run simulation. Please see the document for the detailed description of the command options. In response to exogenous growth in productivity and population, the neoclassical growth model predicts that output, consumption and investment will grow in a balanced.