opgave 10, oef. 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 19:28:56 +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/May/31/t1275334295ev3chbedt8d00q7.htm/, Retrieved Mon, 31 May 2010 21:31:39 +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/May/31/t1275334295ev3chbedt8d00q7.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:

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164 96 73 49 39 59 169 169 210 278 298 245 200 188 90 79 78 91 167 169 289 247 275 203 223 104 107 85 75 99 135 211 335 488 326 346 261 224 141 148 145 223 272 445 560 612 467 404 518 404 300 210 196 186 247 343 464 680 711 610 513 292 273 322 189 257 324 404 677 858 895 664 628 308 324 248 272

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 0.999933893038648 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 96 164 -68 3 73 96.004495273372 -23.0044952733719 4 49 73.00152075728 -24.0015207572799 5 39 49.0015866676051 -10.0015866676051 6 59 39.0006611745033 19.9993388254967 7 169 58.9986779044812 110.001322095519 8 169 168.992728146852 0.00727185314843837 9 210 168.99999951928 41.0000004807201 10 278 209.997289614553 68.0027103854472 11 298 277.995504547453 20.0044954525473 12 245 297.998677563592 -52.9986775635923 13 200 245.003503581529 -45.0035035815294 14 188 200.002975044872 -12.002975044872 15 90 188.000793480207 -98.0007934802074 16 79 90.006478534667 -11.0064785346671 17 78 79.0007276048511 -1.00072760485111 18 91 78.0000661550611 12.9999338449389 19 167 90.9991406138757 76.0008593861243 20 169 166.994975814126 2.00502418587416 21 289 168.999867453944 120.000132546056 22 247 288.992067155876 -41.9920671558755 23 275 247.002775967961 27.9972240320394 24 203 274.998149188593 -71.9981491885929 25 223 203.004759578866 19.9952404211342 26 104 222.998678175414 -118.998678175414 27 107 104.007866641019 2.99213335898092 28 85 106.999802199156 -21.9998021991557 29 75 85.0014543400737 -10.0014543400737 30 99 75.0006611657555 23.9993388342445 31 135 98.9984134766352 36.0015865233648 32 211 134.997620044511 76.0023799554889 33 335 210.994975713606 124.005024286394 34 488 334.991802404652 153.008197595348 35 326 487.989885092995 -161.989885092995 36 346 326.010708659073 19.9892913409267 37 261 345.99867856869 -84.9986785686899 38 224 261.005619004359 -37.0056190043591 39 141 224.002446329025 -83.0024463290253 40 148 141.005487039512 6.9945129604884 41 145 147.999537614002 -2.99953761400207 42 223 145.000198290317 77.9998017096829 43 272 222.994843670123 49.0051563298771 44 445 271.996760418024 173.003239581976 45 560 444.988563281527 115.011436718473 46 612 559.992396943398 52.0076030566021 47 467 611.996561935395 -144.996561935395 48 404 467.009585282116 -63.009585282116 49 518 404.004165372219 113.995834627781 50 404 517.992464081766 -113.992464081766 51 300 404.007535695417 -104.007535695417 52 210 300.006875622143 -90.0068756221425 53 196 210.005950081048 -14.0059500810482 54 186 196.000925890801 -10.0009258908007 55 247 186.000661130821 60.9993388691786 56 343 246.995967519063 96.0040324809371 57 464 342.993653465135 121.006346534865 58 680 463.992000638126 216.007999361874 59 711 679.985720367535 31.0142796324654 60 610 710.997949740215 -100.997949740215 61 513 610.00667666756 -97.0066766675601 62 292 513.006412816625 -221.006412816625 63 273 292.014610062391 -19.0146100623905 64 322 273.001256998093 48.9987430019075 65 189 321.99676084199 -132.99676084199 66 257 189.008792011729 67.9912079882711 67 324 256.995505307841 67.0044946921587 68 404 323.995570536459 80.004429463541 69 677 403.994711150273 273.005288849727 70 858 676.981952449921 181.018047550079 71 895 857.988033446927 37.0119665530734 72 664 894.997553251358 -230.997553251358 73 628 664.015270546325 -36.0152705463252 74 308 628.002380860098 -320.002380860098 75 324 308.021154385024 15.9788456149760 76 248 323.998943687070 -75.9989436870705 77 272 248.005024059233 23.9949759407669 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 78 271.998413765053 76.271369101634 467.725458428472 79 271.998413765053 -4.79227827417157 548.789105804277 80 271.998413765053 -66.9958315938169 610.992659123923 81 271.998413765053 -119.436267341906 663.433094872011 82 271.998413765053 -165.637417446450 709.634244976556 83 271.998413765053 -207.406563208549 751.403390738655 84 271.998413765053 -245.817328689671 789.814156219777 85 271.998413765053 -281.569246345989 825.566073876094 86 271.998413765053 -315.148216564791 859.145044094897 87 271.998413765053 -346.908022374181 890.904849904286 88 271.998413765053 -377.115742513674 921.11257004378 89 271.998413765053 -405.978871303054 949.97569883316

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/1lxbn1275334134.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/1lxbn1275334134.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/2wps81275334134.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/2wps81275334134.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/3wps81275334134.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275334295ev3chbedt8d00q7/3wps81275334134.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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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