*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: Fri, 04 Dec 2009 15:47:36 -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/04/t1259966891muzilewodvuxkzh.htm/, Retrieved Fri, 04 Dec 2009 23:48:15 +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/04/t1259966891muzilewodvuxkzh.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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102.80 118.72 119.01 118.61 120.43 111.83 116.79 131.71 120.57 117.83 130.80 107.46 112.09 129.47 119.72 134.81 135.80 129.27 126.94 153.45 121.86 133.47 135.34 117.10 120.65 132.49 137.60 138.69 125.53 133.09 129.08 145.94 129.07 139.69 142.09 137.29 127.03 137.25 156.87 150.89 139.14 158.30 149.00 158.36 168.06 153.38 173.86 162.47 145.17 168.89 166.64 140.07 128.84 123.40 120.30 129.66 118.12 113.91 131.09 119.14 115.33

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 0.575421884949086 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 112.09 106.263574288625 5.82642571137518 14 129.47 126.311507228401 3.15849277159927 15 119.72 118.534447733525 1.18555226647460 16 134.81 134.566032853922 0.243967146077978 17 135.8 135.872734781201 -0.0727347812006087 18 129.27 129.717493666037 -0.44749366603736 19 126.94 128.101795146917 -1.16179514691723 20 153.45 143.819141094166 9.63085890583429 21 121.86 137.196995719018 -15.3369957190175 22 133.47 125.705934483508 7.76406551649166 23 135.34 144.023195302318 -8.68319530231761 24 117.1 113.829649139404 3.27035086059595 25 120.65 123.208163961331 -2.55816396133098 26 132.49 138.527003687055 -6.03700368705495 27 137.6 124.126853073368 13.4731469266324 28 138.69 148.239039162775 -9.5490391627750 29 125.53 143.774063766198 -18.2440637661984 30 133.09 127.138512032334 5.95148796766628 31 129.08 128.872519387092 0.207480612907858 32 145.94 150.126396894121 -4.18639689412092 33 129.07 125.408158030687 3.66184196931312 34 139.69 134.823840532291 4.86615946770911 35 142.09 144.53473800437 -2.44473800437009 36 137.29 121.773192180732 15.5168078192678 37 127.03 136.185668532610 -9.15566853261012 38 137.25 147.375204229572 -10.1252042295716 39 156.87 138.297969609837 18.5720303901634 40 150.89 155.859448196624 -4.96944819662397 41 139.14 149.286457707526 -10.1464577075265 42 158.3 147.950907445663 10.3490925543371 43 149 148.975802735786 0.0241972642144219 44 158.36 171.023175765537 -12.6631757655367 45 168.06 142.297604644795 25.7623953552047 46 153.38 166.367278926474 -12.9872789264736 47 173.86 163.068853947964 10.7911460520356 48 162.47 152.207703335308 10.2622966646924 49 145.17 152.048495173265 -6.87849517326507 50 168.89 166.425327278975 2.46467272102461 51 166.64 177.842073089522 -11.2020730895223 52 140.07 167.848908560512 -27.7789085605115 53 128.84 145.731871078917 -16.8918710789173 54 123.4 148.777573214764 -25.3775732147641 55 120.3 126.431201949995 -6.13120194999533 56 129.66 136.628126945881 -6.96812694588127 57 118.12 127.632395941283 -9.51239594128324 58 113.91 117.002127082915 -3.09212708291517 59 131.09 126.084147424319 5.00585257568059 60 119.14 116.262787544829 2.87721245517065 61 115.33 108.418468056010 6.91153194398971 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 129.882148583530 108.863664583781 150.900632583279 63 133.207422119426 108.849924119784 157.564920119069 64 123.942694576816 97.5671080632086 150.318281090423 65 122.259346557542 93.5314778239184 150.987215291166 66 129.891139257977 97.784462101679 161.997816414274 67 130.212043482462 96.0097970670925 164.414289897832 68 144.498455771061 105.735156025953 183.261755516169 69 137.420838203399 98.4649286527413 176.376747754057 70 134.409448222772 94.4857032884473 174.333193157097 71 151.029870371034 105.669847774969 196.389892967098 72 135.187409290297 92.3698157698425 178.005002810751 73 126.112645851546 85.3323415240544 166.892950179037

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/1k7wu1259966854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/1k7wu1259966854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/2isvh1259966854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/2isvh1259966854.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/3y8ca1259966854.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966891muzilewodvuxkzh/3y8ca1259966854.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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