, “Volume-Weighted RSI: Money Elow,” Technical Analysis of Stocks & Com-modities (March 1989).(48 MOMENTUM AND OSCILLATORS
 
- _ high + low + closeMoney Flow = volume x rn
14-day positive money flow
M io =oney Ratio 14-day negative money flow
100
M I = ar relloney Flow Index = 100 1 + Money Ratio
Herrick Payoff Index
Using the change in the underlying value of the futures contract, rather than only thechange in price, the Herrick Payoff Index (HPI) combines volume and open interest togenerate an indicator that, as the basic momentum calculation, is not bounded but scaleddown to a manageable value and smoothed using a .10 smoothing factor, s (about 19 days).The daily value is:
M,-M... \ (2x |OL- OL.HP = efx Vx 04,9 x| 1+ (Eten) (Az 1ee- otal]
|M,—M,-3| / \ min(OF,, OF,_ 1)and the index is an exponential smoothing of the individual daily calculations: -.HPlogaay = HPlprevious + 5X (HPhroday ~ HPI previous)
where i is todayt— 1 is the previous dayof is the conversion factor (value of a basis point move)V, is today’s volume. : high + Io(M, - M, -,) is the difference in the mean prices oes| | (vertical bars) are for absolute value|O/, - Of, .,| is the absolute value of the change in open interestmin(OL,, QI, -1) is the smaller of today and the previous open interests is a smoothing constant (default 10) , \
The expression that divides the change in mean prices by the absolute value of the samechange is used to create a +1 or -1 value. This complex formula can also be written in pro-gramming code as
HP = @BigPointValue * volume * ((high-low)/2 - (high{1]-low{1])/2) *(1+ (CChigh-1ow}/2 ~ ChighC1]-lowl1])/2) / @Abs((high-low)/2 -(high[1}-JowLl1])/2))* 2 * (@AbsCopint - opintL1]) /@Lowest(opint,2)))
HPI = @SmoothedAverage(HP,19)
Most analysts who use the Herrick Payoff Index divide the HPI by 100,000 to reducethe value to a more useable level. The final series, when seen along with prices, mayappear volatile and require an interpretation using trendlines. This is due to the fluctua-tions in volume and open interest, which are smoothed over 20 days, rather than longer.The HPI may be helpful, despite the volatility, because it is a combination of factors notincluded in most other indices. It will have patterns that appear to lead price change tocompensate for market noise.
“ From the original Compu Trac manual, which is now the Bridge Telerate division.VELOCITY AND ACCELERATION 149
 
Comments on the Use of Volume
Volume is an important piece of information, but it can be difficult to interpret. It uctu-ates in a much larger range than price, and may be one-third higher or lower from day today. Although it indicates market interest and potential volatility, there are many days forwhich a high or low volume does not have a consistent reaction.
In general, adding volume to an indicator will result in a more volatile, erratic series.Therefore, the first steps in using volume would be
1. Create a long-term, smoothed volume series.
2. Compare current volume for extremes to identify only those exceptional days thatshould be followed by high volatility.
3. Low volume should not be determined by a single day, but by either a few unusu-ally low days together or by a volume decay over a modest time period.
VELOCITY AND ACCELERATION
A method conceptually similar to momentum is derived from the concepts in physics ofvelocity and acceleration, both elements in the science of motion. Velocity, as defined inmechanics, is the rate of change of position with respect to time (also called speed). Thereare two types of velocity, average and instantaneous. The average velocity is simply calcu-lated as the mean velocity over a fixed distance and for a fixed time interval. In workingwith commodity prices, the time interval used will be days and the distance is measured inpoints; so that if silver moved 40 points in 6 days, its average velocity is
-_ 40 2 |.vee 6 3 points per dayIn general, the average velocity is expressed5-2iT
where D is the total elapsed distance over the time interval Z For a geometric interpreta-tion of momentum, D (the change in price) can be related to T (the length of the momen-tum span) to get exactly the same results for average velocity as for slope (see Figure 6-13).
The instantaneous velocity v, which is the velocity calculated at a specific point in time,will be different, To determine the instantaneous velocity, a mathematical technique calleddifferentiation is used. It effectively looks at smaller and smaller time intervals and conse-quently smaller distances on the price curve until the slope calculation is reduced to a sin-gle point. The results of the process of differentiation is called the derivative and isexpressed ~
- , AD 4D
vali aE aeThis shows that the velocity taken at any point is the result of the time interval (f) becom-ing progressively smaller without reaching zero. The rules for differentiation can be foundin any advanced mathematics book. Only the results will be presented. The velocity v, rep-resents the speed or momentum of the price at the point in time #. If v gets larger for , ty,#,,..., then the velocity is increasing; if v gets smaller, the velocity is decreasing. Becausethe velocity also denotes direction, it can be both positive and negative in value and appearsimilar to a momentum indicator. Systems applied to momentum may equally be appliedto velocity. Of course, some of the basic equations have constant velocity and cannot beused for a velocity trading plan, because the values never change. The straight line, simple150 MOMENTUMAND OSCILLATORS
 
 
FIGURE 6-13 (a) Average velocity. (b) Instantaneous velocity.
we
 
(a)
 
{b)
 
and weighted moving averages, and exponential smoothing all have constant velocities.Only those equations with second-order smoothing will work.
When the process of differentiation is reapplied to the equation for velocity, it resultsin the rate of change of the speed with respect to time, or acceleration. This type of accel-eration tells whether the velocity is increasing or decreasing at any point in time. The accel-eration, also called the second derivative, adds another dimension to momentum and mayimprove the timing of trades.
Let’s assume that the velocity and acceleration have been calculated (Table 6-2). Thefollowing are the possible combinations that can occur: ~
es
 
 
Vel Acc Price Movément
+ + Price is moving up at an increasing rate+ 0 Price is moving up at a constant rate
+ Price is moving up at a decreasing rate0 Price is static
Price is moving down at a decreasing ratePrice is moving down at a constant ratePrice is moving down at an increasing rate
lotolVELOCITY AND ACCELERATION 1steS
TABLE 6-2 Equations for Velocity and Acceleration
 
  
Basic Equation Velocity at x,* Acceleration at x,*Straight line Y= at by y=bCurvilinear =a+ bx, +o} v= b+ 2x,Logarithmic (base a) = log, x: log, eX, or = H( In a)
 
 
Logarithmic {natural log) he InnExponential y= erFX tt KaeMoving average % = eat wel a,=0Fame tot Oke ae taterto,Weighted moving average y=SEtOMat Fete wut a0Exponential smoothing Y=K-r tHe) wee a=0de)
* Because velocity and acceleration are time derivatives, all equations implicitly include the factor ~ 7 as part of the right. member.
Using the acceleration feature, a change of velocity (or momentum) can be detected,or the strength of a current price move can be confirmed.
Quick Calculation of Velocity and Acceleration
A less precise but very convenient way of determining velocity and acceleration is the cal-culation of first and second differences. The purpose of these values is to find more sensi-tive indicators of price change, and most traders will find this quick calculation satisfactory.The results can be used in exactly the same way as the formal mathematical results. Con-sider the following examples:
1. A price series 10, 20, 30, 40, . . . is moving higher by a constant value each day. Thefirst differences are 10, 10, 10, . . . , showing a consistent velocity of 10. The seconddifferences, formed by subtracting sequential values in the first-difference series,are 0, 0, 0, ..., showing that there is no change in speed; therefore, the accelera-tion is 0.
2. Another price series is shown with its first and second differences as
 
 
t t 2 3 4 5 6 7 8 9 10 HW 12s 10 15 20 30 45. 50 45 35 25 20 25 40v +5 +5 +10 +15 +5 a) 10 -10 5 +5 +15A 0 $5 +5 -10 -10 -5 0 +5 +10 +10
 
where S is the price seriesV is the Velocity (first differences)Ais the acceleration (second differences)
The original series S has two turns in trend clearly shown by the velocity and accelera-tion, The velocity V continues to be positive through the sixth value as the underlyingprice moves from 10 to 50. Whenever prices change direction, the velocity changessign. The basic upward trend can be associated with a positive velocity and a down-ward trend with a negative one. -
The acceleration, or second difference, shows the change in speed. At the sixthitem, the acceleration becomes negative, even though the velocity was positive,152 MOMENTUM AND OSCILLATORS
 
because prices moved higher at a slower rate. They had been gaining by 5, 10, and 15points each day, but on day 6, the gain was only 5 points. This reversal in accelerationwas a leading indicator of a trend change. A similar situation occurred on day 8, when theacceleration slowed and reversed on day 10, one day ahead of the actual price reversal.
The relationship between velocity and acceleration using first and second differencescan be interpreted using the same logic as previously discussed. Velocity and accelerationare increasingly more sensitive directional indicators; the slightest variation in price move-ment will cause the acceleration to reverse. It is an indicator of great value when it is usedselectively.
OTHER RATE-OF-CHANGE INDICATORS
Projected Crossovers
If moving averages can successfully be used to identify the trend direction, it follows that aprojection of the moving average will be valuable in anticipating when the trends willchange. If a moving average trading strategy used a single trend, the price at which thestandard N-day moving average line would cross the price CP1 is ,
‘‘P,sum of last N — 1 prices _ (S. )
CPL = N-1 “"w-b
To calculate the price at which two moving averages would cross requires the following:
 
Nx (sum of last N— 1 prices) — M x (sum of last M — 1 prices)(=n) ;where N and M are the lengths of the two moving averages.’
The projected crossover price is most useful when it is likely that a.trend change willoccur within a few days, that is, when the two moving averages begin converging andbecome close in value. Acting on the expected price would give the trader a great advan-tage in order execution. A plot of this, however, may not be much different than a simplerelative strength measurement. The difference between the price and the moving averageline constitutes the relative strength. -
The change in the projected crossover is considered a more valuable tool by Lambert.He creates a Market Direction Indicator (MDI) with the following formula:
CP2 =
100 x (Crossover Price previous ~ CfOSSOVEr PriCe day)
MDI= average of past 2 day’s prices
The point at which the MDI crosses the zero line moving higher is a buy signal, and thepoint at which it crosses moving lower is a sell signal.
Combining a Trend and Oscilfator L
Directional Parabolic System
The Directional Parabolic System" is a combination of two of Wilder’s well-known tech-niques, Directional Movement and the Parabolic Time/Price System. Directional Movementis covered fully in Chapter 23, It gained popularity as a method of selecting the commodi-
' Donald R. Lambert, “The Market Directional‘Tndicator,” Technical Analysis of Stocks & Commodities (Novem-ber/December 1983). This article also contains a BASIC computer program to calculate the MDI.
16 J. Welles Wilder, Jr., Chart Trading Workshop 1980 (Irend Research, Greensboro, NC, 1980).OTHER RATE-OF-CHANGE INDICATORS 153idties that were most likely candidates for trend-following systems. The Parabolic Time/PriceSystem is covered in Chapter 17 (‘Adaptive Techniques”). Although a full reading of bothtechniques are necessary, the essence of the combined systems can be understood with thefollowing definitions:
+D114 The 14-day upward Directional IndexD114 The 14-day downward Directional IndexADX The average Directional Movement IndexDPS The Directional Parabolic stop
Although shown as ~DI14, the downward Directional Index is a positive number based onthe sum of those days that closed lower. The ADX is a ratio of those days that closed higherwith those that closed lower over the past 14 days. The ADX is an oscillator based on thescaled ratio of +DI/~DI. The two systems combine according to the following rules:
1. If the ADX is up (the +DM14 is greater than the -DM14), take only long ParabolicSystem trades; if the ADX is down, take only short trades.
2. If the two systems conflict, no trade is entered, A trade may be entered at the timethey agree. .
3. Ifa position is held, the Parabolic stop is used. (The stop is now called the DPS in-stead of the SAR, because it no longer requires a reversal of position.)
4, Ifno position is held, the Directional Movement equilibrium point is used (the highor low of the ‘day on which the +DM14 crosses the -DM14).
Directional Parabolic Revision
In 1980, the entry rules were revised to include an added use of the ADX when it is greaterthan the +DI14 or the —-DI14. Because the ADX serves as an oscillator and indicates turningpoints in the trend, when the ADX exceeds the magnitude of the current +DI14 or —DI14and reverses, the current position should be closed out. If the ADX remains above both the+DI14 and —DI14, the market is extremely strong and liquidation should stop. The ADX isintended to be a leading indicator for liquidation only. Reversal of the current positiononly occurs when the Parabolic stop has been penetrated, and the new trade agrees withthe direction of the Parabolic System. -
The addition of an oscillator to a trend-following system allows trades to be closed outat more favorable positions than the usual trend exits. If the new direction carries throughand the position is reversed, the added feature has worked perfectly; however, if pricesturn back in the original direction, a reentry may not be possible. The revised rules areunclear concerning reentry into a position if prices fail to penetrate the DPS and signal areversal. A reentry might occur if the ADX falls below both the +DI14 and -DI14, indicat-ing that prices are no longer extreme, then turns back in the trend direction. Once reestab-lished, the DPS can be used and additional exits using the revised rules would apply.
Cambridge Hook
A combined indicator that has received some promotion is the Cambridge Hook, used byone commodity trading advisor."’ It is intended to identify an early reversal of the currenttrend by combining the following indicators (applied to an existing uptrend):
1. An outside reversal day (a higher high followed by a lower close)_ 2. Wilder’s RSI must exceed 60% (moderately overbought)3. Volume and open interest must be increasing
'’ Elias Crim, “Are You Watching the ‘Right’ Signals?” Futures June 1985).154 MOMENTUM AND OSCILLATORS,
 
The result is a high likelihood of a downward trend reversal (the opposite applies toupward trend reversals). Protective stops are placed above the high of the hook on the daythat signaled a downard reversal.
MOMENTUM DIVERGENCE
Divergence is a concept familiar to most traders. It is frequently seen in the Dow JonesIndustrials versus the Dow Jones Utilities, when the Utilities indicate a downturn in theeconomy in advance of any sign in the DJIA price pattern. The prices of the S&P 500 arealso watched closely in conjunction with the 30-year U.S. Treasury bonds. When bondprices fall, the S&P can’t be far behind. The underlying relationship of two markets thatmake divergence important can also be represented technically by the slope of trendlinesand the alignment of relative peak prices.
An unsmoothed momentum chart has as many irregular ups and downs as a normalprice chart and is often subjected to the same analysis. Trendlines are drawn across thetops and bottoms of chart sections and can be interpreted in a manner similar to theirprice counterparts (as shown in Figure 6-14), with two significant differences:
1, The trend ofa momentum chart shows the speed of the trend, but allows us to seethe rate of change of price. For example, an unchanged momentum value of +.10 isactually a steady increase of +.10 in the relative price level, that is, a price sequenceof 102.20, 102.30, 102.40, ... . would show a momentum of +.10 and would appearas a horizontal line on a chart. In this example, the change (momentum) is .10, butthe rate of change (acceleration or deceleration) is 0. When the momentum in-creases, ‘the rate of change is positive; a downtrend in the momentum means that
. the rate of change is negative. A steady uptrend in the momentum means that price
 
FIGURE 6-14 Divergence of price and momentum. The trendline drawn across the pricemoves (panel a) and the corresponding momentum (panel 6) and MACD (panel c) indicatorsshows that the directions diverge.
 
ee eaeHOt 95 0102.38 +18 O=10218 H=102.44 L=10218
“eatin.
ee
 
Source: Chart created with TradeStation® by Cmega Research, Inc.MOMENTUM DIVERGENCE 155
eeemovement is accelerating at a steady rate (for example, a gain of .10 the first day, .20the second day, .30 the third, and so on), moving faster and faster, a situation that isnot likely to continue; therefore, these periods are relatively short-lived.
2. The divergence between the price trend and momentum trend creates a verystrong indicator of impending change in the direction of the price trend. A bear-ish divergence occurs when prices continue higher, while momentum moveslower. This is typically seen by drawing a trendline above the rising tops of theprices, as shown in panel a of Figure 6-14, and above the falling tops of the mo-mentum indicator, seen in panels 6 and c of Figure 6-14. The reason for this pat-tern is that prices are actually rising at a slower rate, causing the new price peaksto be farther apart.
Figure 6-14 gives three examples of divergence using two different momentum indica-tors, the difference between prices and a single moving average (Figure 6-14, panel b), andan MACD, the difference between two moving averages (Figure 6-14, panel c). The classicexample is in the center of the chart, where prices make new highs near the close of 10/22,while both of the momentum indicators show lower peaks. In classic divergence the trend-lines drawn on the price chart must be in absolute contrast to the direction of those drawnon the momentum-chart. That is, one must be going up and the other down. The failure ofmomentum to make a corresponding high peak indicates a downturn in prices.
On the left side of Figure 6-14 is a bullish divergence, in which prices make new lowswhile the momentum indicators rise. In this case, the MACD is much stronger than thestandard momentum. On the far right, a bullish divergence appears in the center panel butnot in the MACD indicator. Standard momentum indicates a modest rise in value while theMACD declines quickly. Not all changes in price direction are identified by the divergenceof price and momentum, but it remains a valuable tool.
We can distinguish between a stronger and weaker divergence by measuring the dif-ference in the relative angles of the two trendlines, but mostly by the momentum trend-line. In a bearish divergence situation, the price trend is normally increasing at a slow rate,and becoming slower. When the momentum drops quickly there is a strong divergenceand the price rise is quickly ending.
Slope Divergence
To change an interpretive analysis to one that can be computerized, there are two tech-niques, one using slopes and the other based on the analysis of peaks. A comparisonbetween the rate at which prices and a momentum indicator are rising or falling will giveenough information to automatically identify a divergence. Using a linear regression fea-ture in either a spreadsheet @S1ope) or a strategy testing program (@LinearRegS|ope), theslope of any time interval can be found for both momentum and price over the sameperiod. Because momentum is a detrended series, the period compared should not be toolong; otherwise, the slope of the trendline will be zero, a horizontal line. Instead of thetrendlines that appear above and below prices and momentum in Figure 6-14, the regres-sion lines will pass through the center of the price movement.
Divergence can be any combination of conflicting directions between the slope ofprice and the slope of momentum, including prices rising faster than momentum, momen-tum rising faster than prices, or the opposite. However, classic analysis has focused onmomentum as a leading indicator of a change in the price trend, which limits the combi-nations to: .
1. Prices rising and momentum falling (a bearish divergence)2. Prices falling and momentum rising (a bullish divergence)156 MOMENTUM AND OSCILLATORS
 
The strength of a bearish divergence, which can be used to select which situations are bestfor trading, can be determined by the momentum slope provided prices are rising, or thenet of the rising slope of prices and the falling slope of momentum. In the second case,the difference between the slopes must be converted to a common denominator, becausethe angle of price movement can cover a far wider range than the angle of momentummovement.
Divergence Using Peak Comparisons
The identification of divergence for a short-term trader is very different from the slopetechnique that applies to the major moves seen in the Dow Jones Industrials and Utilities.In this application, the peaks (or valleys) of any momentum indicator are comparedagainst the corresponding peaks (or valleys) of the price series (upon which the momen-tum was calculated). If the momentum peaks are declining and the price peaks are risingthere is a divergence. In Figure 6-14 the ups and downs between the peaks are ignored,and only the points at which the prices form swing highs and lows are compared with cor-responding momentum values,
It is easier to find divergence by looking at a chart on a quote screen than to programit into a computer. Translating what you see into a systematic analysis of divergence signalsis very difficult. There are a number of steps necessary for signaling a bearish divergence:
1. Identify each momentum peak and record its value, MP,. The standard ap-proach to finding a momentum peak is to locate each momentum value that ishigher than the previous 7 values and higher than the next 7 values. In addition, thefirst momentum peak of a sequence must be above a threshold level, for example80, to assure that an overbought situation has occurred. It seems reasonable that ailmomentum peak values should be greater than some level, for example 50, to avoidhaving already reached the correction objective before a position can be entered(see Step 4).
2, Identify the price peaks corresponding to each momentum peak, PP,. This isdone in the same way as Step 1 or the corresponding value of the price can be used,assuming that it produced a peak.
3, Compare the last momentum peak, MP,, with the previous momentum peak,MP,_,, and their corresponding prices, PP; and PP,_,. A bearish divergence ex-ists if PP, > PP; and MP, < MP,_;. A stronger divergence exists if MP,., — MP, islarger.
4, Enter a short position when the divergence is identified, provided prices havenot already reached the correction level or anticipated profit. This fourth steppoints out a problem in this method of finding a divergence. The need to wait anumber of days after a momentum high will cause many of the signals to be too late.Although the price may have been higher at the time of the second peak, the lagneeded to recognize the next declining momentum peak gives the price a chance tocorrect before a signal can be generated.
5. Exit the short position when the current momentum moves above the lastmomentum peak. This new momentum high indicates that the divergence, usedas the entry criteria, has disappeared and there is no basis for this trade. The exactprice at which this occurs cannot be calculated in advance.
6. Exit the short position when the market has corrected or an objective hasbeen reached. Once the momentum has declined to the midpoint level of 50 forthe RSI and stochastic, it should be considered neutral and cannot be expected tocontinue on to negative values. A price objective can be set using volatility or sup-port levels.MOMENTUM SMOOTHING 7
 
Single, Double, and Triple Divergences
In fewer cases, double and triple divergences will occur. A double divergence is one inwhich three momentum peaks are declining and price is rising in each case. Most often,the second momentum peak is only slightly lower than the first, and the last peak drops offindicating that price is soon to follow. Multiple divergences are expected to be more reli-able than single, and represent a prolonged period in which prices are rising at a slowerand slower rate.
Alternating Divergence Peaks
A common pattern is that there is a lower momentum peak between two declining peaks.For example, the first momentum peak is at 90, the next at 60, and the last at 75. Whenstudying the chart manually, most analysts will ignore the lower peak in the middle andconsider the 90-75 divergence. This combination can be automated by looking at the mostrecent momentum peak, i, and the one back 2, i — 2, along with their correspondingprices.
Converting a Divergence into a Trend Trade
Divergence trades represent a clear chart pattern of slowing price direction. At the sametime they are countertrend trades and have a higher degree of risk. Before the October1987 stock plunge, there were numerous divergence signals in the S&B both long-termand short-term, and many traders posted losses trying to sell what might have been the topof the market. Most gave up before the decline. If, in fact, the greatest opportunities comewhen the divergence is strong, that is, the decline in the momentum peaks is large, thenthe best results will come from entering a short position, then holding that short when‘along trend turns to a short one. By entering the trend trade early (and exiting the old.longPosition), a divergence can become a large profit rather than a small one. :
MOMENTUM SMOOTHING
When Blau’s work on double smoothing was discussed in the section “True StrengthIndex,” it was still being compared with other momentum indicators. The most importantpart of his work, however, is in using price change as a substitute, or proxy, for prices them-selves, then smoothing them to define the trend. A long-term moving average, applied toprices, produces a lag of one-half the period of the moving average; that is, a 200-day mov-ing average has a lag of 100 days.
The same moving average technique applied to price change, or momentum, givesvery different results because price changes, also called first differences, remove theunderlying trend and make price movement more sensitive. Applying a long-term moving,average to momentum is an excellent substitute for price, yet it oscillates around the aver-age value of zero in a manner similar to other momentum indicators.
Double Smoothing of Momentum
Double smoothing of momentum is an extension of normal moméntum smoothing, andresults in a value that has less noise than the original momentum series, and retains its low-lag characteristics, provided that one of the smoothing periods is very large. Doublesmoothing of momentum can be a smooth substitute for price, without a significant lag(see Figure 6-12). The shape of Blau’s True Strength Index (TSD, first smoothed over a300-day period, then smoothed again over a 5-day period, closely approximates the resultof a 5-day exponential smoothing (EMA). When applied using the same smoothing peri-ods, this can be very useful for identifying divergence between two markets. In Figure 6-15the trend of the TSI line is still up at the end of February 1994, making a new high in both158 MOMENTUM AND OSCILLATORS
 
 
FIGURE 6-15 Double-smoothed momentum applied to the Dow Jones Average andDow Jones Utilities, showing divergence. 1
 
     
Dow Industials-Dailp07/01/96 C=5729.980 +75.351 O=5670.141 H=5749.191 L=5637,262
or IN tye
\True Strength Index 18.84
     
   
  
070196 C=220.660 +350 0=220.720 H-221 60 L=218.840
eta Mae
  
 
 
Source: Chart created with TradeStation® by Omega Research, Inc:
the prices and indicator, while the utilities are steadily heading lower. In December 1994there is a turn up in the TSI for the utilities that will lead the DJIA throughout 1995.
TSI(close,300,5) =
100 x @SmoothedAverage(@SmoothedAverage(close — close[1]),300),5)@SmoothedAverage(@SmoothedAverage(@abs(close ~ close{1]),300),5)
When the 5-day momentum is replaced by a 1-day momentum, or the daily pricechanges, the second smoothing can be any length, and the result is a very effective substi-tute for a moving average of price with the significant added advantages of a detrendedseries, lower noise, and less lag. When plotted, the series fluctuates around the value zerounless there has been a strong trend during the full period, as in the stock index.
 
SOME FINAL COMMENTS ON MOMENTUM —_
Momentum and oscillators are not the only tools for determining overbought and oversoldconditions. Because they can be very different from either a charting technique or movingaverages, they have taken their place as timing indicators within other more structured sys-tems, When the time interval for calculation is small, these indicators can be highly unsta-ble, jumping from frequent overbought signals to just as frequent oversold ones. Bothfaster and slower speeds have the problem of risk control. The method implies that a pos