*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: Tue, 01 Dec 2009 06:02:40 -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/01/t1259672609ign9ui3u2fjohwh.htm/, Retrieved Tue, 01 Dec 2009 14:03:33 +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/01/t1259672609ign9ui3u2fjohwh.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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149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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 0.854437321125315 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 147 149.288219344397 -2.28821934439665 14 137 137.177584627027 -0.177584627026732 15 132 131.813009578090 0.186990421909599 16 125 124.931497762185 0.0685022378148687 17 123 123.182653686134 -0.182653686133733 18 117 117.321542481451 -0.321542481451047 19 114 113.800867796673 0.199132203327082 20 111 108.989385381903 2.01061461809660 21 112 111.620445807089 0.379554192910774 22 144 147.648085339519 -3.64808533951887 23 150 152.372496893666 -2.3724968936659 24 149 150.421482435404 -1.42148243540382 25 134 139.411758519791 -5.41175851979096 26 123 125.732170895332 -2.73217089533193 27 116 118.720865136260 -2.72086513625989 28 117 110.138791424190 6.86120857581037 29 111 114.270120056966 -3.27012005696565 30 105 106.262273153879 -1.26227315387895 31 102 102.307675073961 -0.307675073961406 32 95 97.7915659352005 -2.79156593520051 33 93 95.9518846525865 -2.95188465258649 34 124 122.660029759549 1.33997024045141 35 130 130.653539756426 -0.653539756425857 36 124 130.233414809786 -6.23341480978584 37 115 116.133800319431 -1.13380031943082 38 106 107.668146841762 -1.66814684176249 39 105 102.157618193940 2.84238180606027 40 105 100.128900536713 4.87109946328657 41 101 101.392730999395 -0.39273099939534 42 95 96.5511775195222 -1.55117751952220 43 93 92.7193740558354 0.280625944164555 44 84 88.7222787488008 -4.72227874880082 45 87 85.1155657719593 1.88443422804066 46 116 114.542680260747 1.45731973925284 47 120 121.888524286081 -1.88852428608079 48 117 119.589642046601 -2.5896420466008 49 109 109.755994811509 -0.755994811508714 50 105 101.904630629795 3.09536937020516 51 107 101.154190867906 5.84580913209362 52 109 101.915979829881 7.08402017011852 53 109 104.208376755375 4.79162324462484 54 108 103.305590536572 4.69440946342796 55 107 104.819822038987 2.18017796101297 56 99 100.985479211867 -1.98547921186665 57 103 100.971239531668 2.02876046833154 58 131 135.526496637099 -4.52649663709906 59 137 138.072947082428 -1.07294708242770 60 135 136.297600139550 -1.29760013955027 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 126.741319375095 120.730490886514 132.752147863676 62 119.051526714288 111.336387163918 126.766666264658 63 115.650338489133 106.521277130421 124.779399847845 64 111.230583689697 101.00551139822 121.455655981173 65 107.031425237685 95.879654992898 118.183195482473 66 102.080982306999 90.2098149136444 113.952149700353 67 99.3556428513328 86.6655226424536 112.045763060212 68 93.4804344180823 80.413172565572 106.547696270593 69 95.601963506728 81.2700500731836 109.933876940272 70 125.139112970981 105.822930274115 144.455295667848 71 131.729924465956 110.732392899101 152.727456032812 72 130.858161293145 99.2467189532628 162.469603633027

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/1l3ef1259672558.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/1l3ef1259672558.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/271a81259672558.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/271a81259672558.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/3pqjy1259672558.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672609ign9ui3u2fjohwh/3pqjy1259672558.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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