*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 26 Jan 2010 18:30:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir.htm/, Retrieved Wed, 27 Jan 2010 02:33:27 +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/2010/Jan/27/t1264556003ueggivinw1v7cir.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

1 4 -3 -3 0 6 -1 0 -1 1 -4 -1 -1 0 3 0 8 8 8 8 11 13 5 12 13 9 11 7 12 11 10 13 14 10 13 12 13 17 15 6 9 6 11 12 13 11 16 16 19 14 15 12 14 16 13 13 15 12 13 12 15 10 8 11 8 13 9 8 8 6 8 6 12 16

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.715895076963664 beta 0 gamma 0.990005082021168 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 -1 -2.91239316239316 1.91239316239316 14 0 -0.689299333195945 0.689299333195945 15 3 2.53318764501435 0.466812354985652 16 0 -0.570269375831298 0.570269375831298 17 8 7.52533797522378 0.474662024776218 18 8 7.51083382767033 0.489166172329673 19 8 5.29837979461261 2.70162020538739 20 8 9.04481071182932 -1.04481071182932 21 11 7.77585684589279 3.22414315410721 22 13 12.2713593696986 0.728640630301447 23 5 7.89701058882804 -2.89701058882804 24 12 8.96874261606209 3.03125738393791 25 13 11.7807157035141 1.21928429648594 26 9 13.1636024334441 -4.16360243344406 27 11 12.8493430573329 -1.84934305733293 28 7 8.1168606511552 -1.11686065115520 29 12 14.9777688897305 -2.97776888973049 30 11 12.4957659605931 -1.49576596059315 31 10 9.48459537182584 0.515404628174158 32 13 10.6121842382125 2.38781576178749 33 14 13.0013394308575 0.99866056914247 34 10 15.2017316182060 -5.20173161820597 35 13 5.56208859829139 7.43791140170861 36 12 15.6999565737289 -3.69995657372891 37 13 13.1834415409131 -0.183441540913101 38 17 12.0481044036421 4.95189559635794 39 15 18.9105060896457 -3.91050608964569 40 6 12.9084691124501 -6.90846911245007 41 9 15.0997844190741 -6.09978441907414 42 6 10.7995819668727 -4.79958196687273 43 11 5.98889829848031 5.01110170151969 44 12 10.8615788794307 1.13842112056930 45 13 11.9655774227417 1.03442257725828 46 11 12.4476161776176 -1.4476161776176 47 16 9.05061912874011 6.94938087125989 48 16 15.7060545286148 0.293945471385197 49 19 17.0378280254382 1.96217197456183 50 14 18.8829172720305 -4.88291727203047 51 15 16.2119386174891 -1.21193861748908 52 12 11.2985697866030 0.701430213397018 53 14 19.1652295139376 -5.16522951393758 54 16 15.8997721731816 0.100227826818426 55 13 17.3562432723403 -4.35624327234029 56 13 14.4336369685910 -1.43363696859104 57 15 13.6670606048898 1.33293939511016 58 12 13.6646946612886 -1.66469466128865 59 13 12.4740762367539 0.525923763246066 60 12 12.6590471641812 -0.659047164181242 61 15 13.7777921821201 1.22220781787992 62 10 13.1678585306438 -3.16785853064381 63 8 12.7572009630589 -4.75720096305892 64 11 5.84396056440337 5.15603943559663 65 8 15.2495651920529 -7.24956519205291 66 13 11.9729327320262 1.02706726797375 67 9 12.8394728650157 -3.83947286501575 68 8 11.1088477421315 -3.10884774213148 69 8 9.92113821246912 -1.92113821246912 70 6 6.7460636345231 -0.7460636345231 71 8 6.82923362658582 1.17076637341418 72 6 7.14255297975992 -1.14255297975992 73 12 8.44429034472116 3.55570965527884 74 16 8.27012576477607 7.72987423522393 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 75 15.2140745302603 8.58380906201755 21.8443399985031 76 14.4947415906877 6.34057769811172 22.6489054832636 77 16.7198966437353 7.28483663361315 26.1549566538574 78 20.9611218726291 10.3993830952203 31.5228606500379 79 19.7236006484856 8.14429606617856 31.3029052307927 80 20.9471347550606 8.43273252333356 33.4615369867876 81 22.3190955171362 8.93476767353233 35.7034233607401 82 20.8498620520723 6.64879869636945 35.0509254077752 83 22.0062731282231 7.03295789610755 36.9795883603386 84 20.8307900957378 5.12314426168875 36.5384359297869 85 24.2719338464477 7.86278681634483 40.6810808765506 86 22.7263019556079 5.64443803906907 39.8081658721467

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/1q1jw1264555824.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/1q1jw1264555824.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/2189l1264555824.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/2189l1264555824.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/3hsou1264555824.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264556003ueggivinw1v7cir/3hsou1264555824.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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