verbetering

*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Thu, 10 Dec 2009 10:13:00 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv.htm/, Retrieved Thu, 10 Dec 2009 18:13:42 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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102.86 102.55 102.28 102.26 102.57 103.08 102.76 102.51 102.87 103.14 103.12 103.16 102.48 102.57 102.88 102.63 102.38 101.69 101.96 102.19 101.87 101.6 101.63 101.22 101.21 101.49 101.64 101.66 101.77 101.82 101.78 101.28 101.29 101.37 101.12 101.51 102.24 102.94 103.09 103.46 103.64 104.39 104.15 105.21 105.8 105.91 105.39 105.46 104.72 103.14 102.63 102.32 101.93 100.62 100.6 99.63 98.9 98.32 99.22 98.81

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.819828902860289 beta 0.380658228872049 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 102.48 102.641041747874 -0.161041747874194 14 102.57 102.545592990979 0.0244070090205071 15 102.88 102.837940082573 0.0420599174272809 16 102.63 102.648872734969 -0.0188727349688236 17 102.38 102.424351424615 -0.044351424614689 18 101.69 101.741505230615 -0.0515052306153052 19 101.96 102.078938340214 -0.118938340213560 20 102.19 101.596091894191 0.593908105808836 21 101.87 102.449108102370 -0.579108102369659 22 101.6 102.054102773546 -0.454102773545628 23 101.63 101.365358516229 0.264641483771214 24 101.22 101.479890564252 -0.259890564251990 25 101.21 100.373903427511 0.836096572488913 26 101.49 101.201661785410 0.288338214589800 27 101.64 101.867100895439 -0.227100895439463 28 101.66 101.521685353881 0.138314646119412 29 101.77 101.54507234628 0.224927653719917 30 101.82 101.290503505736 0.529496494264279 31 101.78 102.480721223983 -0.700721223982526 32 101.28 101.855579183130 -0.575579183130472 33 101.29 101.378370479508 -0.0883704795080575 34 101.37 101.400813155179 -0.0308131551786772 35 101.12 101.314660205805 -0.194660205805420 36 101.51 100.941014072638 0.568985927361908 37 102.24 100.950924563253 1.28907543674656 38 102.94 102.433690719131 0.506309280869218 39 103.09 103.639610313187 -0.549610313187472 40 103.46 103.444384803987 0.0156151960129591 41 103.64 103.692209483583 -0.0522094835825868 42 104.39 103.479699699620 0.910300300379731 43 104.15 105.109346253215 -0.959346253215443 44 105.21 104.554402238713 0.655597761286984 45 105.8 105.829732951958 -0.0297329519584082 46 105.91 106.589733235301 -0.679733235301129 47 105.39 106.410749210747 -1.02074921074669 48 105.46 105.711338035133 -0.251338035132790 49 104.72 105.116760392585 -0.396760392584511 50 103.14 104.499455246477 -1.35945524647687 51 102.63 102.827331842622 -0.197331842621836 52 102.32 101.974212448107 0.345787551893338 53 101.93 101.537660601359 0.392339398641354 54 100.62 101.064479808940 -0.444479808939647 55 100.6 100.022325667924 0.577674332076143 56 99.63 100.262918510549 -0.632918510548976 57 98.9 99.20254370552 -0.302543705519966 58 98.32 98.3732347798924 -0.0532347798924491 59 99.22 97.6011398544248 1.61886014557516 60 98.81 98.9661073748992 -0.156107374899179 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 98.2533040371124 97.131288856674 99.375319217551 62 97.7345435613244 96.0421666742657 99.4269204483831 63 97.7289902862882 95.3819957589803 100.075984813596 64 97.550182733870 94.481777828534 100.618587639206 65 97.1555323399272 93.3103004670476 101.000764212807 66 96.4202885937162 91.7583609879724 101.08221619946 67 96.248739913619 90.6930365262981 101.804443300940 68 95.9448718458424 89.4516267574393 102.438116934245 69 95.8020655033174 88.3115404178762 103.292590588759 70 95.699728834307 87.1598850147617 104.239572653852 71 95.7182796388638 86.069524657624 105.367034620104 72 95.3891336499251 83.9709845580115 106.807282741839

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/1g4vg1260465178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/1g4vg1260465178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/2fv931260465178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/2fv931260465178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/32k571260465178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260465218205sr33bl7h3etv/32k571260465178.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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