triple exponential smoothing prijzen energiegrondstoffen - Charlotte De Saeger

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 05:52:43 -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/06/t1244289301r1efsssxunbp3rq.htm/, Retrieved Sat, 06 Jun 2009 13:55:01 +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/06/t1244289301r1efsssxunbp3rq.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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106,8 114,3 105,7 90,1 91,6 97,7 100,8 104,6 95,9 102,7 104 107,9 113,8 113,8 123,1 125,1 137,6 134 140,3 152,1 150,6 167,3 153,2 142 154,4 158,5 180,9 181,3 172,4 192 199,3 215,4 214,3 201,5 190,5 196 215,7 209,4 214,1 237,8 239 237,8 251,5 248,8 215,4 201,2 203,1 214,2 188,9 203 213,3 228,5 228,2 240,9 258,8 248,5 269,2 289,6 323,4 317,2 322,8 340,9 368,2 388,5 441,2 474,3 483,9 417,9 365,9 263 199,4 157,2

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 0.925208409968674 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 113.8 94.7435442960424 19.0564557039576 14 113.8 108.948077901234 4.85192209876554 15 123.1 118.463999628398 4.6360003716015 16 125.1 119.907200673507 5.19279932649277 17 137.6 132.276859461182 5.32314053881791 18 134 130.210418212023 3.78958178797703 19 140.3 134.256614453362 6.04338554663798 20 152.1 144.736247276670 7.36375272332981 21 150.6 137.995391906789 12.6046080932107 22 167.3 156.945712015124 10.3542879848757 23 153.2 163.396038159528 -10.1960381595276 24 142 154.849623944533 -12.8496239445329 25 154.4 148.506319551579 5.89368044842075 26 158.5 147.866585481524 10.6334145184755 27 180.9 164.631824042517 16.2681759574834 28 181.3 175.567955731245 5.73204426875478 29 172.4 191.802646718712 -19.402646718712 30 192 164.863473774272 27.1365262257281 31 199.3 190.949383604587 8.35061639541266 32 215.4 205.702345114928 9.69765488507204 33 214.3 195.994258402797 18.3057415972030 34 201.5 222.934924962338 -21.434924962338 35 190.5 197.381223101414 -6.88122310141443 36 196 191.773554538566 4.22644546143371 37 215.7 205.235897139547 10.4641028604525 38 209.4 206.861121223847 2.5388787761529 39 214.1 218.775207632589 -4.67520763258923 40 237.8 208.622057878781 29.1779421212193 41 239 247.186330674228 -8.1863306742282 42 237.8 231.585567729447 6.21443227055343 43 251.5 236.778527966979 14.7214720330210 44 248.8 259.315992533638 -10.5159925336380 45 215.4 228.561073660509 -13.1610736605085 46 201.2 223.326442855265 -22.1264428552645 47 203.1 198.173013434133 4.92698656586674 48 214.2 204.416505407971 9.78349459202849 49 188.9 224.341293039953 -35.4412930399533 50 203 183.868147120199 19.1318528798014 51 213.3 210.250323687874 3.04967631212565 52 228.5 209.543227719543 18.9567722804574 53 228.2 235.442320602473 -7.2423206024728 54 240.9 222.079535109339 18.8204648906605 55 258.8 239.51220672625 19.2877932737498 56 248.5 264.519262667103 -16.0192626671034 57 269.2 228.342639234705 40.8573607652953 58 289.6 273.686900365972 15.9130996340282 59 323.4 284.58714912856 38.8128508714401 60 317.2 323.680321250667 -6.48032125066726 61 322.8 328.121135389173 -5.32113538917292 62 340.9 316.821947449979 24.0780525500209 63 368.2 351.586354518257 16.6136454817434 64 388.5 362.745133782865 25.7548662171350 65 441.2 397.375466857159 43.824533142841 66 474.3 428.681795065001 45.6182049349993 67 483.9 470.79967917269 13.1003208273100 68 417.9 491.223973199139 -73.3239731991388 69 365.9 393.507586970987 -27.6075869709869 70 263 375.641652170156 -112.641652170156 71 199.4 269.142256092473 -69.7422560924728 72 157.2 204.481052461895 -47.2810524618951 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 166.06560235588 112.580258339886 219.550946371874 74 163.855755274616 89.8080827077046 237.903427841527 75 169.564447098225 81.0666452948311 258.062248901619 76 167.884758001092 64.2499565571834 271.519559445001 77 173.005434776591 60.0763456583152 285.934523894867 78 169.314695425893 46.5561396524902 292.073251199296 79 168.406144036728 35.8288892855833 300.983398787873 80 168.740672618867 34.9129216350159 302.568423602718 81 157.999834058789 15.9586367148078 300.041031402771 82 157.171728060068 7.1164318170824 307.227024303054 83 156.742167049015 -1.67086003569091 315.155194133721 84 157.2 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/1znvt1244289158.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/1znvt1244289158.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/2jvmn1244289158.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/2jvmn1244289158.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/3ekfc1244289158.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244289301r1efsssxunbp3rq/3ekfc1244289158.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; 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')

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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