exponential smoothing - opgave 10 - Vanovermeire Bart

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 08:08:44 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h.htm/, Retrieved Sun, 01 Jun 2008 14:09:52 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

Text written by user:

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.185475284794843 beta 0.000362009975189055 gamma 0.521962133305563 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 39722.9017575777 -2020.90175757770 14 30364 31535.1647279220 -1171.16472792205 15 32609 33590.6706490098 -981.670649009757 16 30212 30845.0542818759 -633.05428187587 17 29965 30291.5608338424 -326.560833842421 18 28352 28469.5184451801 -117.518445180067 19 25814 25831.2286456269 -17.2286456268739 20 22414 22218.8079229484 195.192077051648 21 20506 20072.5399434037 433.460056596261 22 28806 27930.4449264666 875.555073533356 23 22228 21566.2431248708 661.756875129231 24 13971 13746.8693916781 224.130608321868 25 36845 37213.4050139222 -368.405013922165 26 35338 29947.1989476151 5390.80105238488 27 35022 33308.6175017057 1713.38249829426 28 34777 31165.8203156701 3611.17968432987 29 26887 31520.5411419808 -4633.54114198077 30 23970 28958.9890191581 -4988.98901915809 31 22780 25492.0388690565 -2712.03886905648 32 17351 21581.2380713670 -4230.23807136697 33 21382 18854.0296661702 2527.9703338298 34 24561 26884.760927283 -2323.76092728299 35 17409 20297.5845264531 -2888.58452645312 36 11514 12446.0767867257 -932.07678672567 37 31514 32744.2952985218 -1230.29529852177 38 27071 28263.5475890451 -1192.54758904512 39 29462 28693.3350317845 768.664968215468 40 26105 27404.5074091275 -1299.50740912755 41 22397 23992.1600755122 -1595.16007551224 42 23843 22093.2602175134 1749.73978248663 43 21705 21025.8101504192 679.189849580791 44 18089 17487.4969484943 601.503051505708 45 20764 18432.1220109149 2331.87798908514 46 25316 23929.205603231 1386.794396769 47 17704 18076.7317399466 -372.731739946608 48 15548 11701.2390141251 3846.7609858749 49 28029 33682.2332964645 -5653.23329646454 50 29383 28310.749161143 1072.25083885702 51 36438 30049.5703336388 6388.42966636116 52 32034 28761.9441145584 3272.05588544160 53 22679 25730.3147471643 -3051.31474716425 54 24319 24963.3452032993 -644.345203299283 55 18004 22866.9428489642 -4862.9428489642 56 17537 18177.4902171702 -640.490217170161 57 20366 19623.4814012916 742.518598708433 58 22782 24395.3863212825 -1613.38632128246 59 19169 17424.4224011483 1744.57759885167 60 13807 13167.5829631344 639.417036865627 61 29743 29499.3786647026 243.621335297357 62 25591 28109.0855152350 -2518.08551523496 63 29096 31165.2654727371 -2069.26547273713 64 26482 27303.0021100247 -821.002110024696 65 22405 21530.9386521874 874.061347812596 66 27044 22431.6796050798 4612.32039492025 67 17970 19629.5503743844 -1659.55037438441 68 18730 17383.6798500639 1346.32014993611 69 19684 19765.1142051539 -81.1142051538809 70 19785 23314.0381640939 -3529.03816409394 71 18479 17568.5563000246 910.443699975363 72 10698 12888.4569955773 -2190.45699557732 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 27245.5103222072 24298.6735269787 30192.3471174356 74 24823.0195252185 21764.5473174073 27881.4917330298 75 28275.3351838739 25018.2405341873 31532.4298335605 76 25480.8261514185 22176.9497044052 28784.7025984318 77 20816.6481598158 17541.8136275926 24091.4826920390 78 22940.02389854 19452.4402507169 26427.6075463630 79 17177.6691322863 13845.4495559018 20509.8887086708 80 16556.0822544388 13135.4716237339 19976.6928851438 81 17936.3113768610 14302.8783731128 21569.7443806092 82 19798.5316238417 15897.4397206946 23699.6235269888 83 16793.3755880923 13050.9727845655 20535.778391619 84 11047.7166824143 9412.9780783711 12682.4552864575

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/1t2pv1212329318.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/1t2pv1212329318.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/2nkmg1212329318.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/2nkmg1212329318.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/3ges51212329318.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123293926j1i9y49he92w3h/3ges51212329318.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; 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')

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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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