Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Maple package TimeS for time series analysis has a new feature and an improvement in forecasting by phase space reconstruction. An optional argument in the computational routines that allows the researcher to choose the different number of steps ahead to forecast. This update extends the running of the package with this new feature for the current versions of the Maple software too.#R##N#New version program summary#R##N#Program Title:TimeS#R##N##R##N#Program Files doi:10.17632/nhtmjc8yp8.1#R##N##R##N#Licensing provisions: GNU General Public License 3#R##N##R##N#Programming language: Maple17#R##N##R##N#Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 1115#R##N##R##N#Does the new version supersede the previous version?: Yes.#R##N##R##N#Nature of problem: Time series analysis and improving forecast capability.#R##N##R##N#Solution method: The method of solution is published in [1].#R##N##R##N#Reasons for the new version:#R##N##R##N#For a phenomenon described by an unknown low-dimensional dynamical system defined by a set of coupled differential equations ẋi=fi(x),i=1,…,n, one generates a map MM for which the time variable is increased by δt:xi(P+1)=Fi(x(P),δt).#R##N##R##N#Though another map M¯ that approaches MM, X¯i(P+1) is close to xi(P+1)xi(P+1) when δt→0δt→0 [1]. #R##N##R##N#equation(1)#R##N##R##N#X¯i(P+1)=F¯i(x(P),δt)=∑k=0N(δt)kk!Xk[xi(P)].#R##N##R##N##R##N##R##N#In the reconstruction’s scheme by delays method [2], x(P) is state vector reconstructed. Its components have regular spacings in the time series. The approach X¯i(P+1) corresponds to the prediction for the value xi(P+1)xi(P+1) [3].#R##N##R##N#If one applies δt→τδt′δt→τδt′ in the mapping (1), then #R##N##R##N#equation(2)#R##N##R##N#X¯i(P+τ)=F¯i(x(P),τδt′)=∑k=0N(τδt′)kk!Xk[xi(P)].#R##N##R##N##R##N##R##N#This application enables the choose for different times of prediction, e.g., in chaotic time series [4]. So, other entries beyond the nearest neighbor to the last known value can be predicted and analyzed.#R##N##R##N#Here,  extend the capacity of forecasting and analysis of the computational routines by means the optional argument called PT. It corresponds to parameter ττ in the mapping (2). The researcher can include this option in the commands GfiTS, ForecasTS and IforecasTS.#R##N##R##N#In the NIforecasTS command, our package was already trying to tackle a similar calculation. But it employs the global mapping corresponding to the next entry in the time series, i.e., only the parameter τ=1τ=1 take part in the global fitting. The program predicts the NN steps by the next step (corresponding to N=1N=1) and using it as the N=2N=2 data and so on, up to the actual value of NN that  are trying to forecast. Because this different conception, the routines NIforecasTS, AnalysTS and GrafiTS have not changed with respect to their running.#R##N##R##N#The use of the commands in this version of the TimeS package closely follows the previous version. But the programming logistic in the GifTS routine required an update for the correct running of the new features in the current versions of the Maple software.  considered our internal procedure gerpoly deprecated–it does not work properly in the Maple 17 release–and it has been deleted in this version. The polynomials are now generated inside the GfiTS routine. There is a change in the optional argument that selects the part of the time series for the global mapping. The choosing now refers to the last vector to be used in the global mapping. The argument IniPoint was substituted by Final for all routines in this update. The goal of this new option is to relate more easily the global mapping with the position on the time series of interest in the forecasting. Another slight modification is present for the error calculation by the optional argument Poptions. Instead of the percent error, this analysis option now prints the actual error.#R##N##R##N#Let us consider the same time series of the original paper [1]. It is stored in the file ‘ts37.txt’ and corresponds to the dynamical variable XX of the Lorenz System [5]. Below,  present the Maple worksheet for the reconstruction of phase space, the global mapping, the forecasting and the improvement of the forecast. The respective routines in this example are VecTS, GfiTS, ForecasTS and IforecasTS. The date to be forecast is dat[402]. #R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (202 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#−0.03991323747X12+0.1157254791X1X2−0.05432130896X1X3−0.03977733053X22+0.03040753173X2X3−0.005038168581X32+1.487438057X1−0.3816889428X2+0.09738575830X3#R##N##R##N##R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (69 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.2926021229.2316024609.2926021229.231602460#R##N##R##N##R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (69 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.2926021229.278554589.9.2926021229.278554589.#R##N##R##N#Thus, for the forecasting and analysis of the second entry in a given time series (i.e.,  τ=2τ=2), the argument is PT=2 and so on. In order to compare the same prediction by the command NIforecasTS,  put its respective prompt too: #R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (70 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.333733567.9.333733567.#R##N##R##N#The argument Nsteps=2 specifies the parameter τ=2τ=2 and the map Mapag[1] corresponds to τ=1τ=1 above. In this application, the prediction with the new feature in the IforecasTS is more accurate–9.279 compared to 9.333 for the true value 9.293–than the result of the command NIforecasTS. Besides being an alternative for improved accuracy, the new feature enlarges the possibilities in time series analysis by the TimeS package.#R##N##R##N#Summary of revisions:#R##N##R##N#Modification of the way the polynomials needed are generated, making the running of the program compatible with the new version (release 17 up) Maple;#R##N##R##N#The introduction of the possibility of the calculating for the prediction NN steps ahead that improved our previous similar calculation;#R##N##R##N#Instructions to use the TimeS package (README.pdf), computational routines (TimeS.txt) and test file (TimeS.mw).#R##N##R##N#Restrictions:#R##N##R##N#If the time series that is being analyzed presents a great amount of noise or if the dynamical system behind the time series is of high dimensionality (Dim≫3Dim≫3), then the method may not work ll.#R##N##R##N#Unusual features:#R##N##R##N#Our implementation can, in the cases where the dynamics behind the time series is given by a system of low dimensionality, greatly improve the forecast.#R##N##R##N#Running time:#R##N##R##N#It depends strongly on the command used.#R##N##R##N##R##N#[1]#TAB##R##N#H. Carli, L. Duarte, L. da Mota, A maple package for improved global mapping forecast, Computer Physics Communications 185 (3) (2014) 1115–1129.#R##N##R##N#[2]#TAB##R##N#N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712–716.#R##N##R##N#[3]#TAB##R##N#H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Cambridge nonlinear science series, Cambridge University Press, 2004.#R##N##R##N#[4]#TAB##R##N#J.D. Farmer, J.J. Sidorowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (1987) 845–848.#R##N##R##N#[5]#TAB##R##N#E. Lorenz, Deterministic nonperiodic flow, Journal of the Atmospheric Sciences 20 (2) (1963) 130–141.
['P.R.L. Alves', 'L. G. S. Duarte', 'L. A. C. P. da Mota']
I am writing a research paper on a idea A new method for improved global mapping forecast
[{"from": "human", "value": "I am writing a research paper on a idea A new method for improved global mapping forecast"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Maple package TimeS for time series analysis has a new feature and an improvement in forecasting by phase space reconstruction. An optional argument in the computational routines that allows the researcher to choose the different number of steps ahead to forecast. This update extends the running of the package with this new feature for the current versions of the Maple software too.#R##N#New version program summary#R##N#Program Title:TimeS#R##N##R##N#Program Files doi:10.17632/nhtmjc8yp8.1#R##N##R##N#Licensing provisions: GNU General Public License 3#R##N##R##N#Programming language: Maple17#R##N##R##N#Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 1115#R##N##R##N#Does the new version supersede the previous version?: Yes.#R##N##R##N#Nature of problem: Time series analysis and improving forecast capability.#R##N##R##N#Solution method: The method of solution is published in [1].#R##N##R##N#Reasons for the new version:#R##N##R##N#For a phenomenon described by an unknown low-dimensional dynamical system defined by a set of coupled differential equations x\u0307i=fi(x),i=1,\u2026,n, one generates a map MM for which the time variable is increased by \u03b4t:xi(P+1)=Fi(x(P),\u03b4t).#R##N##R##N#Though another map M\u00af that approaches MM, X\u00afi(P+1) is close to xi(P+1)xi(P+1) when \u03b4t\u21920\u03b4t\u21920 [1]. #R##N##R##N#equation(1)#R##N##R##N#X\u00afi(P+1)=F\u00afi(x(P),\u03b4t)=\u2211k=0N(\u03b4t)kk!Xk[xi(P)].#R##N##R##N##R##N##R##N#In the reconstruction\u2019s scheme by delays method [2], x(P) is state vector reconstructed. Its components have regular spacings in the time series. The approach X\u00afi(P+1) corresponds to the prediction for the value xi(P+1)xi(P+1) [3].#R##N##R##N#If one applies \u03b4t\u2192\u03c4\u03b4t\u2032\u03b4t\u2192\u03c4\u03b4t\u2032 in the mapping (1), then #R##N##R##N#equation(2)#R##N##R##N#X\u00afi(P+\u03c4)=F\u00afi(x(P),\u03c4\u03b4t\u2032)=\u2211k=0N(\u03c4\u03b4t\u2032)kk!Xk[xi(P)].#R##N##R##N##R##N##R##N#This application enables the choose for different times of prediction, e.g.,\u00a0in chaotic time series [4]. So, other entries beyond the nearest neighbor to the last known value can be predicted and analyzed.#R##N##R##N#Here,  extend the capacity of forecasting and analysis of the computational routines by means the optional argument called PT. It corresponds to parameter \u03c4\u03c4 in the mapping (2). The researcher can include this option in the commands GfiTS, ForecasTS and IforecasTS.#R##N##R##N#In the NIforecasTS command, our package was already trying to tackle a similar calculation. But it employs the global mapping corresponding to the next entry in the time series, i.e.,\u00a0only the parameter \u03c4=1\u03c4=1 take part in the global fitting. The program predicts the NN steps by the next step (corresponding to N=1N=1) and using it as the N=2N=2 data and so on, up to the actual value of NN that  are trying to forecast. Because this different conception, the routines NIforecasTS, AnalysTS and GrafiTS have not changed with respect to their running.#R##N##R##N#The use of the commands in this version of the TimeS package closely follows the previous version. But the programming logistic in the GifTS routine required an update for the correct running of the new features in the current versions of the Maple software.  considered our internal procedure gerpoly deprecated\u2013it does not work properly in the Maple 17 release\u2013and it has been deleted in this version. The polynomials are now generated inside the GfiTS routine. There is a change in the optional argument that selects the part of the time series for the global mapping. The choosing now refers to the last vector to be used in the global mapping. The argument IniPoint was substituted by Final for all routines in this update. The goal of this new option is to relate more easily the global mapping with the position on the time series of interest in the forecasting. Another slight modification is present for the error calculation by the optional argument Poptions. Instead of the percent error, this analysis option now prints the actual error.#R##N##R##N#Let us consider the same time series of the original paper [1]. It is stored in the file \u2018ts37.txt\u2019 and corresponds to the dynamical variable XX of the Lorenz System [5]. Below,  present the Maple worksheet for the reconstruction of phase space, the global mapping, the forecasting and the improvement of the forecast. The respective routines in this example are VecTS, GfiTS, ForecasTS and IforecasTS. The date to be forecast is dat[402]. #R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (202 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#\u22120.03991323747X12+0.1157254791X1X2\u22120.05432130896X1X3\u22120.03977733053X22+0.03040753173X2X3\u22120.005038168581X32+1.487438057X1\u22120.3816889428X2+0.09738575830X3#R##N##R##N##R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (69 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.2926021229.2316024609.2926021229.231602460#R##N##R##N##R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (69 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.2926021229.278554589.9.2926021229.278554589.#R##N##R##N#Thus, for the forecasting and analysis of the second entry in a given time series (i.e.,\u00a0 \u03c4=2\u03c4=2), the argument is PT=2 and so on. In order to compare the same prediction by the command NIforecasTS,  put its respective prompt too: #R##N##R##N##R##N##TAB##R##N##R##N##R##N##R##N#Figure options#R##N##R##N##R##N##R##N#Download full-size image#R##N#Download high-quality image (70 K)#R##N#Download as PorPoint slide#R##N##R##N##R##N##R##N##R##N##R##N##R##N##R##N#9.333733567.9.333733567.#R##N##R##N#The argument Nsteps=2 specifies the parameter \u03c4=2\u03c4=2 and the map Mapag[1] corresponds to \u03c4=1\u03c4=1 above. In this application, the prediction with the new feature in the IforecasTS is more accurate\u20139.279 compared to 9.333 for the true value 9.293\u2013than the result of the command NIforecasTS. Besides being an alternative for improved accuracy, the new feature enlarges the possibilities in time series analysis by the TimeS package.#R##N##R##N#Summary of revisions:#R##N##R##N#Modification of the way the polynomials needed are generated, making the running of the program compatible with the new version (release 17 up) Maple;#R##N##R##N#The introduction of the possibility of the calculating for the prediction NN steps ahead that improved our previous similar calculation;#R##N##R##N#Instructions to use the TimeS package (README.pdf), computational routines (TimeS.txt) and test file (TimeS.mw).#R##N##R##N#Restrictions:#R##N##R##N#If the time series that is being analyzed presents a great amount of noise or if the dynamical system behind the time series is of high dimensionality (Dim\u226b3Dim\u226b3), then the method may not work ll.#R##N##R##N#Unusual features:#R##N##R##N#Our implementation can, in the cases where the dynamics behind the time series is given by a system of low dimensionality, greatly improve the forecast.#R##N##R##N#Running time:#R##N##R##N#It depends strongly on the command used.#R##N##R##N##R##N#[1]#TAB##R##N#H.\u00a0Carli, L.\u00a0Duarte, L.\u00a0da\u00a0Mota, A maple package for improved global mapping forecast, Computer Physics Communications 185\u00a0(3) (2014) 1115\u20131129.#R##N##R##N#[2]#TAB##R##N#N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712\u2013716.#R##N##R##N#[3]#TAB##R##N#H.\u00a0Kantz, T.\u00a0Schreiber, Nonlinear Time Series Analysis, Cambridge nonlinear science series, Cambridge University Press, 2004.#R##N##R##N#[4]#TAB##R##N#J.D. Farmer, J.J. Sidorowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (1987) 845\u2013848.#R##N##R##N#[5]#TAB##R##N#E.\u00a0Lorenz, Deterministic nonperiodic flow, Journal of the Atmospheric Sciences 20\u00a0(2) (1963) 130\u2013141."}]