Exponential smoothing consumptieprijsindex

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 18:04:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m.htm/, Retrieved Sun, 16 Jan 2011 19:02:34 +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/2011/Jan/16/t1295200954kajej70ki2zsc1m.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

98,6 100,1 98,8 98,3 102,8 103,6 105,2 100,1 98,2 98,4 97,4 98,4 100,3 101,1 104,1 107,3 110,1 112,6 114,3 115,3 109,9 108,2 103,2 101,8 105,6 108,2 109,8 114,6 117,2 116,5 116,1 112,1 106,8 106,9 104,5 103 105,9 107,7 107,1 112,5 114,5 114,6 113,1 112,8 111,9 112 112,4 110 112,3 109,6 111,9 110,8 110,4 110,8 114 108,4 110,5 105,1 102,3 104,3 103,4 102,4 104,5 107,3 110,1 111,8 111,8 105,7 106 106,4 107,1 111,5 109,6 109,9 109,3 111,4 112,9 115,5 118,4 116,2 113,3 113,8 114,1 117,1 115,5 115,2 114,2 115,3 118,8 118 118,1 111,8 112 114,3 115 118,5 117,6 119,1 120,6 123,6 122,7 123,8 123,1 124,5 120,7 118,7 119 122,3 118,6 118,1 118,2 120,8 119,7 119,7 117,1 114,5 116,5 116,4 114,9 115,5

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 0.952517560780428 beta 0 gamma 0.374732084602801 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 100.3 96.0956755050505 4.20432449494946 14 101.1 99.8878684177092 1.21213158229078 15 104.1 102.921611702484 1.17838829751557 16 107.3 106.348213915953 0.951786084047157 17 110.1 109.404806875114 0.695193124885819 18 112.6 112.183657201368 0.416342798631561 19 114.3 112.326064361703 1.97393563829721 20 115.3 108.993772721031 6.30622727896878 21 109.9 112.838064946522 -2.93806494652156 22 108.2 109.643673156913 -1.44367315691304 23 103.2 106.589382456259 -3.38938245625938 24 101.8 103.681769479805 -1.88176947980459 25 105.6 103.109992697268 2.49000730273224 26 108.2 105.216027712315 2.98397228768540 27 109.8 109.936879983091 -0.136879983090779 28 114.6 112.106634085128 2.49336591487192 29 117.2 116.627043296340 0.57295670366041 30 116.5 119.284499647016 -2.78449964701640 31 116.1 116.405762719262 -0.305762719262262 32 112.1 110.979103662894 1.12089633710600 33 106.8 109.719791628103 -2.91979162810317 34 106.9 106.569395497356 0.330604502644263 35 104.5 105.170515043207 -0.670515043207473 36 103 104.879496272427 -1.87949627242708 37 105.9 104.387672629764 1.51232737023554 38 107.7 105.571239554811 2.12876044518912 39 107.1 109.421957599299 -2.32195759929917 40 112.5 109.557187374263 2.94281262573732 41 114.5 114.471532257647 0.0284677423528308 42 114.6 116.550613440744 -1.95061344074445 43 113.1 114.510272413776 -1.41027241377645 44 112.8 108.056933297881 4.74306670211908 45 111.9 110.175905401345 1.72409459865489 46 112 111.506727378932 0.49327262106786 47 112.4 110.244978050435 2.15502194956522 48 110 112.623821247039 -2.62382124703942 49 112.3 111.483366369288 0.816633630711905 50 109.6 112.015241103453 -2.41524110345301 51 111.9 111.458525389575 0.441474610425246 52 110.8 114.319649947310 -3.51964994730972 53 110.4 113.026530241747 -2.62653024174656 54 110.8 112.541465046846 -1.74146504684649 55 114 110.709955930287 3.29004406971326 56 108.4 108.843238359275 -0.443238359275142 57 110.5 105.968446661598 4.53155333840212 58 105.1 109.951522136435 -4.85152213643458 59 102.3 103.628329769884 -1.32832976988441 60 104.3 102.604188401966 1.69581159803396 61 103.4 105.639476344401 -2.2394763444007 62 102.4 103.202847287306 -0.802847287305596 63 104.5 104.232795093475 0.267204906524682 64 107.3 106.857443642474 0.4425563575262 65 110.1 109.354286473380 0.745713526620278 66 111.8 112.097090823293 -0.297090823293118 67 111.8 111.730900133966 0.0690998660337954 68 105.7 106.729749630265 -1.02974963026527 69 106 103.384813078329 2.61518692167115 70 106.4 105.37556101144 1.02443898855991 71 107.1 104.712013646182 2.38798635381784 72 111.5 107.281537779823 4.21846222017699 73 109.6 112.649673399997 -3.04967339999706 74 109.9 109.466879638455 0.433120361545008 75 109.3 111.693147980377 -2.39314798037726 76 111.4 111.786883749015 -0.386883749014771 77 112.9 113.499064446974 -0.599064446974438 78 115.5 114.942389342180 0.557610657820305 79 118.4 115.396832524606 3.00316747539389 80 116.2 113.170880901699 3.02911909830122 81 113.3 113.756943151736 -0.45694315173597 82 113.8 112.793128755252 1.00687124474820 83 114.1 112.137109667532 1.96289033246804 84 117.1 114.334292386980 2.76570761302027 85 115.5 118.189330389361 -2.68933038936144 86 115.2 115.411739696433 -0.211739696432915 87 114.2 116.973479169590 -2.77347916959022 88 115.3 116.740640649132 -1.44064064913178 89 118.8 117.445324022735 1.35467597726462 90 118 120.770201925111 -2.77020192511111 91 118.1 118.098359448810 0.00164055118968065 92 111.8 113.013862483689 -1.21386248368944 93 112 109.496382086886 2.50361791311403 94 114.3 111.378600027138 2.92139997286236 95 115 112.563213806116 2.43678619388353 96 118.5 115.226075338706 3.27392466129390 97 117.6 119.468136457908 -1.86813645790784 98 119.1 117.516831655937 1.58316834406324 99 120.6 120.742671031687 -0.142671031687485 100 123.6 123.039438915232 0.56056108476804 101 122.7 125.700039692473 -3.00003969247309 102 123.8 124.803579696823 -1.00357969682265 103 123.1 123.863795845572 -0.763795845572133 104 124.5 118.028579590260 6.47142040974016 105 120.7 121.897611956789 -1.19761195678892 106 118.7 120.261777126474 -1.56177712647398 107 119 117.167463163538 1.83253683646230 108 122.3 119.269661938772 3.03033806122771 109 118.6 123.188208855713 -4.58820885571336 110 118.1 118.707397062168 -0.607397062168431 111 118.2 119.815976226602 -1.6159762266022 112 120.8 120.721907784676 0.0780922153237924 113 119.7 122.859594032883 -3.15959403288261 114 119.7 121.846679124973 -2.14667912497278 115 117.1 119.822339515138 -2.72233951513807 116 114.5 112.250313623353 2.24968637664685 117 116.5 111.961613610092 4.53838638990806 118 116.4 115.782938272308 0.617061727691592 119 114.9 114.824402264983 0.0755977350171406 120 115.5 115.274398401753 0.225601598246982 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 116.385826305389 111.837896432622 120.933756178156 122 116.346195373694 110.065292298675 122.627098448712 123 118.015385062046 110.385455786623 125.645314337469 124 120.490705241235 111.716772368336 129.264638114133 125 122.496398505302 112.711309064306 132.281487946299 126 124.511075389536 113.809951491623 135.212199287448 127 124.521242506926 112.976541125398 136.065943888454 128 119.630761028152 107.300059211189 131.961462845114 129 117.239918516927 104.170401134521 130.309435899332 130 116.668577556929 102.899831720101 130.437323393758 131 115.112645044334 100.678503600197 129.546786488472 132 115.493302058699 100.423115711493 130.563488405906

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/17r6u1295201078.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/17r6u1295201078.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/2e3k81295201078.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/2e3k81295201078.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/3upbk1295201078.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295200954kajej70ki2zsc1m/3upbk1295201078.ps (open in new window)

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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