Kelly Janbroers - 2de zit - Stap 27/B

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 08 Jul 2010 15:42:46 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy.htm/, Retrieved Thu, 08 Jul 2010 17:43:00 +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/2010/Jul/08/t1278603776x4yshytbx37ybjy.htm/}, year = {2010}, } @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 = {2010}, 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 «

268 267 266 264 262 261 262 264 265 265 266 268 260 264 265 262 258 265 273 273 270 263 260 257 248 248 237 228 225 231 243 250 246 240 236 235 225 230 225 221 231 234 249 257 253 252 245 239 229 232 222 218 223 221 230 234 237 226 215 211 203 202 187 179 181 172 182 180 175 163 160 151 145 140 125 122 124 108 115 116 104 98 101 91

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 1 beta 0.0475220280630285 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 266 266 0 4 264 265 -1 5 262 262.952477971937 -0.952477971936958 6 261 260.907214287025 0.0927857129748304 7 262 259.911623652281 2.08837634771902 8 264 261.010867531683 2.98913246831654 9 265 263.152917168727 1.8470828312731 10 265 264.240694290869 0.759305709130558 11 266 264.276778038087 1.72322196191288 12 268 265.35866904052 2.64133095948 13 260 267.4841904445 -7.48419044450014 14 264 259.128526536168 4.87147346383244 15 265 263.360028834824 1.63997116517589 16 262 264.437963590558 -2.43796359055813 17 258 261.322106616391 -3.32210661639101 18 265 257.164233372538 7.83576662746151 19 273 264.536604894104 8.46339510589593 20 273 272.938802593835 0.0611974061650358 21 270 272.941710818688 -2.94171081868814 22 263 269.801914754609 -6.80191475460907 23 260 262.478673970758 -2.47867397075822 24 257 259.360882356761 -2.36088235676078 25 248 256.248688439149 -8.24868843914925 26 248 246.856694035661 1.14330596433916 27 237 246.911026253783 -9.9110262537828 28 228 235.440034186017 -7.44003418601713 29 225 226.086468672639 -1.08646867263931 30 231 223.034837477889 7.96516252211146 31 243 229.413358154791 13.5866418452091 32 250 242.059022929841 7.94097707015874 33 246 249.436394265017 -3.43639426501721 34 240 245.273089840319 -5.27308984031944 35 236 239.022501916949 -3.0225019169489 36 235 234.878866496031 0.121133503968906 37 225 233.884623005806 -8.88462300580608 38 230 223.462407701995 6.53759229800528 39 225 228.773087346645 -3.77308734664518 40 221 223.593782583874 -2.59378258387366 41 231 219.470520775133 11.5294792248666 42 234 230.018425010410 3.98157498959037 43 249 233.2076375288 15.7923624712000 44 257 248.958122621338 8.04187737866212 45 253 257.340288943806 -4.34028894380612 46 252 253.134029610817 -1.13402961081690 47 245 252.080138223827 -7.08013822382733 48 239 244.743675696464 -5.74367569646449 49 229 238.470724578832 -9.47072457883218 50 232 228.020656539620 3.97934346038031 51 222 231.209763011216 -9.20976301121632 52 218 220.772096394943 -2.77209639494345 53 223 216.640360752270 6.35963924773046 54 221 221.942583707071 -0.942583707070924 55 230 219.897790217692 10.1022097823083 56 234 229.377867714465 4.6221322855348 57 237 233.597520814649 3.40247918535059 58 226 236.759213525980 -10.7592135259795 59 215 225.247913878862 -10.2479138788618 60 211 213.760912227923 -2.76091222792303 61 203 209.629708079548 -6.62970807954812 62 202 201.314650906142 0.685349093857866 63 187 200.347220085013 -13.3472200850134 64 179 184.71293311757 -5.71293311757 65 181 176.441442949635 4.55855705036538 66 172 178.658074825709 -6.65807482570901 67 182 169.341669606996 12.6583303930041 68 180 179.943219139163 0.0567808608366533 69 175 177.945917480825 -2.94591748082547 70 163 172.805921507630 -9.80592150763033 71 160 160.339924230561 -0.339924230560854 72 151 157.323770341737 -6.32377034173683 73 145 148.023251950093 -3.02325195009269 74 140 141.879580886079 -1.87958088607877 75 125 136.790259390464 -11.7902593904638 76 122 121.229962352840 0.770037647160208 77 124 118.266556103518 5.73344389648227 78 108 120.539020985264 -12.5390209852642 79 115 103.943141278120 11.0568587218805 80 116 111.468585628590 4.53141437141032 81 104 112.683927629513 -8.68392762951305 82 98 100.271249777006 -2.27124977700602 83 101 94.163315381365 6.836684618635 84 91 97.4882084996698 -6.48820849966984 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 87.1798756732697 74.3685115015469 99.9912398449926 86 83.3597513465395 64.8062490078778 101.913253685201 87 79.5396270198092 56.2792418178234 102.800012221795 88 75.719502693079 48.2365699427932 103.202435443365 89 71.8993783663487 40.470538172337 103.328218560360 90 68.0792540396185 32.8774350756663 103.281073003571 91 64.2591297128882 25.3973090102854 103.120950415491 92 60.439005386158 17.9921860204390 102.885824751877 93 56.6188810594277 10.6364552352157 102.601306883640 94 52.7987567326975 3.31203661472124 102.285476850674 95 48.9786324059672 -3.99428286974069 101.951547681675 96 45.158508079237 -11.2924234230024 101.609439581476

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/1d2lp1278603764.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/1d2lp1278603764.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/2d2lp1278603764.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/2d2lp1278603764.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/3ob2a1278603764.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/08/t1278603776x4yshytbx37ybjy/3ob2a1278603764.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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