Exponential Smoothing Prijs kleurentelevisie - Tjitse Voortman

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 11:46:39 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s.htm/, Retrieved Tue, 02 Jun 2009 19:48:30 +0200

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/Jun/02/t1243964910yjzeacjoq5mez1s.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:

» Textbox « » Textfile « » CSV «

666.27 664.45 660.76 660.40 660.69 660.69 662.23 661.41 659.02 655.43 652.59 652.59 648.20 645.84 644.67 642.71 640.14 640.14 639.64 630.28 614.57 614.70 615.08 615.08 614.43 604.55 598.98 594.05 593.05 593.05 593.34 584.72 580.70 577.08 569.92 569.92 568.86 559.38 548.22 545.61 545.33 530.30 527.76 521.41 1601.93 1577.49 1551.43 1551.43 1516.88 1485.95 1438.22 1385.06 1329.49 1329.49 1276.16 1242.34 1181.59 1160.21 1135.18 1135.18 1084.96 1077.35 1061.13 1029.98 1013.08 1013.08 996.04 975.02 951.89 944.40 932.47 932.47 920.44 900.18 886.90

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 0.987057390298826 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 664.45 666.27 -1.81999999999994 3 660.76 664.473555549656 -3.71355554965623 4 660.4 660.808063100083 -0.408063100082813 5 660.69 660.405281401438 0.284718598562222 6 660.69 660.686314998304 0.00368500169588515 7 662.23 660.689952306461 1.54004769353867 8 661.41 662.210067763781 -0.800067763781385 9 659.02 661.420354964801 -2.40035496480107 10 655.43 659.051066857454 -3.62106685745368 11 652.59 655.476866055038 -2.88686605503779 12 652.59 652.62736358061 -0.0373635806099628 13 648.2 652.590483582241 -4.3904835822409 14 645.84 648.256824315404 -2.41682431540437 15 644.67 645.87128001383 -1.20128001383068 16 642.71 644.685547698361 -1.97554769836074 17 640.14 642.735568742806 -2.59556874280599 18 640.14 640.173593433191 -0.0335934331907310 19 639.64 640.140434786694 -0.500434786694314 20 630.28 639.646476932125 -9.36647693212512 21 614.57 630.401226655208 -15.8312266552075 22 614.7 614.774897387689 -0.0748973876891341 23 615.08 614.700969367657 0.379030632343529 24 615.08 615.075094354461 0.00490564553922468 25 614.43 615.079936508144 -0.649936508144492 26 604.55 614.438411874555 -9.88841187455546 27 598.98 604.677981855457 -5.69798185545676 28 594.05 599.05374675524 -5.0037467552396 29 593.05 594.114761541297 -1.06476154129655 30 593.05 593.063780793054 -0.0137807930537974 31 593.34 593.050178359426 0.289821640574246 32 584.72 593.336248951623 -8.6162489516231 33 580.7 584.831516747269 -4.13151674726896 34 577.08 580.753472608734 -3.67347260873373 35 569.92 577.127544322223 -7.20754432222293 36 569.92 570.013284433066 -0.0932844330664011 37 568.86 569.921207344008 -1.06120734400827 38 559.38 568.873734792465 -9.49373479246549 39 548.22 559.502873704025 -11.2828737040253 40 545.61 548.366029830659 -2.75602983065880 41 545.33 545.645670218423 -0.315670218422952 42 530.3 545.334085596431 -15.0340855964314 43 527.76 530.494580302089 -2.7345803020886 44 521.41 527.795392605546 -6.38539260554649 45 1601.93 521.492643644282 1080.43735635572 46 1577.49 1587.94632099012 -10.4563209901194 47 1551.43 1577.62533208149 -26.1953320814853 48 1551.43 1551.76903595912 -0.339035959123294 49 1516.88 1551.43438801009 -34.5543880100936 50 1485.95 1517.32722395748 -31.3772239574776 51 1438.22 1486.35610316319 -48.136103163188 52 1385.06 1438.84300679578 -53.7830067957766 53 1329.49 1385.75609246551 -56.2660924655133 54 1329.49 1330.21823007419 -0.728230074191288 55 1276.16 1329.49942519762 -53.3394251976229 56 1242.34 1276.85035136202 -34.5103513620179 57 1181.59 1242.78665400833 -61.196654008329 58 1160.21 1182.38204440785 -22.1720444078476 59 1135.18 1160.49696411705 -25.3169641170477 60 1135.18 1135.50766758539 -0.327667585385598 61 1084.96 1135.18424087367 -50.2242408736695 62 1077.35 1085.61003274717 -8.26003274716572 63 1061.13 1077.45690637997 -16.3269063799653 64 1029.98 1061.34131277690 -31.3613127769036 65 1013.08 1030.38589723099 -17.3058972309879 66 1013.08 1013.30398347339 -0.223983473389353 67 996.04 1013.08289893068 -17.0428989306756 68 975.02 996.260579589036 -21.2405795890363 69 951.89 975.294908531448 -23.4049085314476 70 944.4 952.192920596214 -7.79292059621423 71 932.47 944.50086072971 -12.0308607297090 72 932.47 932.625710734794 -0.155710734793843 73 920.44 932.472015303267 -12.0320153032667 74 900.18 920.595725677989 -20.4157256779888 75 886.9 900.444232769216 -13.5442327692165 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 887.075297718434 636.355313584583 1137.79528185228 77 887.075297718434 534.790764110012 1239.35983132686 78 887.075297718434 456.55436350579 1317.59623193108 79 887.075297718434 390.494833975696 1383.65576146117 80 887.075297718434 332.245558837597 1441.90503659927 81 887.075297718434 279.555815461114 1494.59477997575 82 887.075297718434 231.084593898763 1543.06600153810 83 887.075297718434 185.956416448323 1588.19417898854 84 887.075297718434 143.562306675859 1630.58828876101 85 887.075297718434 103.458395128462 1670.69220030841 86 887.075297718434 65.30931387612 1708.84128156075 87 887.075297718434 28.8543387714091 1745.29625666546

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/1vce91243964794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/1vce91243964794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/2i0wd1243964794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/2i0wd1243964794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/37o5q1243964794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243964910yjzeacjoq5mez1s/37o5q1243964794.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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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Software written by Ed van Stee & Patrick Wessa

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