Tijdreeks A - stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 22:18:46 +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/Aug/20/t12822564946yjtsq0mnku42ff.htm/, Retrieved Fri, 20 Aug 2010 00:21:37 +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/Aug/20/t12822564946yjtsq0mnku42ff.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:

Van Boxel Dieter

Dataseries X:

» Textbox « » Textfile « » CSV «

356 355 354 352 372 371 356 346 347 347 348 350 353 350 343 346 373 363 349 350 353 356 355 346 349 348 342 342 379 375 363 361 363 373 367 360 358 367 357 346 386 383 367 354 363 370 361 354 363 366 353 351 389 385 364 348 347 352 342 338 343 354 329 320 353 345 324 310 314 313 310 301 294 296 274 269 292 287 271 256 260 265 263 256 246 245 220 224 240 238 222 203 209 214 216 214 206 196 169 177 193 183 164 142 141 137 140 146 136 124 105 114 135 123 100 74 64 57 62 64

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.604067171997709 beta 0.0703089588431605 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 353 355.767282849865 -2.76728284986484 14 350 350.972607223685 -0.972607223685145 15 343 342.696726558656 0.303273441344231 16 346 345.002598260693 0.997401739307008 17 373 371.633548826925 1.36645117307523 18 363 362.170776180986 0.829223819013862 19 349 354.412772362754 -5.4127723627538 20 350 341.244794669971 8.75520533002879 21 353 348.206591605717 4.79340839428289 22 356 352.027220040909 3.97277995909059 23 355 356.048526761376 -1.04852676137563 24 346 358.101527882073 -12.1015278820725 25 349 353.163049124451 -4.16304912445094 26 348 348.14586671249 -0.145866712490204 27 342 340.845472496173 1.15452750382741 28 342 343.896945517829 -1.89694551782912 29 379 368.510220257027 10.4897797429729 30 375 364.509319221991 10.4906807780089 31 363 360.473742403607 2.52625759639295 32 361 358.441902544933 2.55809745506747 33 363 360.743363663273 2.25663633672707 34 373 363.262610127859 9.7373898721409 35 367 369.548773316264 -2.54877331626426 36 360 366.872520210674 -6.8725202106736 37 358 369.459801567944 -11.4598015679443 38 367 362.253322192032 4.74667780796767 39 357 358.951708187976 -1.95170818797573 40 346 359.695540552882 -13.695540552882 41 386 383.100963830452 2.89903616954751 42 383 374.189164943507 8.81083505649275 43 367 365.649181674783 1.35081832521655 44 354 362.664797879166 -8.6647978791657 45 363 357.37638706177 5.62361293823028 46 370 364.259489099363 5.74051090063733 47 361 362.628920802497 -1.62892080249725 48 354 358.155358793036 -4.1553587930357 49 363 359.87159098948 3.1284090105197 50 366 367.994159890913 -1.99415989091261 51 353 357.74376080876 -4.74376080876027 52 351 351.699854617891 -0.699854617890765 53 389 390.328664004253 -1.3286640042528 54 385 381.119998782689 3.88000121731147 55 364 366.461864237559 -2.46186423755927 56 348 356.884978325654 -8.88497832565406 57 347 356.723802955268 -9.7238029552684 58 352 353.252208419052 -1.25220841905212 59 342 343.611797838406 -1.61179783840635 60 338 337.135788903484 0.864211096516442 61 343 343.386242183586 -0.386242183586432 62 354 345.924702118619 8.07529788138129 63 329 340.31550124668 -11.3155012466801 64 320 330.948138572574 -10.9481385725744 65 353 358.547533529034 -5.54753352903435 66 345 347.600449935565 -2.60044993556534 67 324 326.538974496149 -2.53897449614863 68 310 313.558180460462 -3.55818046046221 69 314 313.964775078003 0.035224921996587 70 313 317.794813879693 -4.79481387969338 71 310 305.295429512083 4.70457048791684 72 301 302.816092223163 -1.81609222316257 73 294 305.002581965368 -11.0025819653684 74 296 301.745160956462 -5.74516095646209 75 274 280.558513439322 -6.55851343932233 76 269 272.311739771828 -3.31173977182817 77 292 298.815311980841 -6.81531198084105 78 287 287.062628017994 -0.0626280179935748 79 271 268.756571786857 2.24342821314326 80 256 258.400939301071 -2.40093930107082 81 260 258.403949679111 1.59605032088905 82 265 259.113799023346 5.88620097665410 83 263 256.409140039636 6.59085996036379 84 256 252.542827425169 3.45717257483091 85 246 253.26125691526 -7.26125691525982 86 245 252.552456822219 -7.55245682221889 87 220 231.830451932749 -11.8304519327494 88 224 220.875750867249 3.12424913275075 89 240 243.998508396941 -3.99850839694082 90 238 236.357885995989 1.64211400401120 91 222 221.994522913074 0.00547708692633364 92 203 209.830381508620 -6.83038150861972 93 209 206.783332018890 2.21666798110974 94 214 207.898149750457 6.10185024954319 95 216 205.485556445498 10.5144435545020 96 214 203.483084454116 10.5169155458839 97 206 204.543132671038 1.45686732896226 98 196 208.052531955809 -12.0525319558091 99 169 185.455340566486 -16.4553405664857 100 177 176.226748266972 0.773251733028019 101 193 190.027725369628 2.97227463037163 102 183 188.548670045437 -5.54867004543664 103 164 171.547067692069 -7.54706769206913 104 142 154.219947267134 -12.2199472671343 105 141 148.160059889812 -7.16005988981192 106 137 142.079166652793 -5.07916665279262 107 140 132.929680915740 7.07031908426043 108 146 128.670249561701 17.3297504382987 109 136 130.784286195767 5.21571380423288 110 124 129.657060689831 -5.6570606898311 111 105 112.851974654600 -7.85197465459972 112 114 110.706191524176 3.29380847582370 113 135 119.396696857702 15.6033031422985 114 123 122.756141378609 0.243858621390601 115 100 111.812161686028 -11.8121616860280 116 74 93.5276024625379 -19.5276024625379 117 64 80.9839341426352 -16.9839341426352 118 57 66.5668433464246 -9.56684334642462 119 62 55.7468704734617 6.25312952653834 120 64 52.9738768675282 11.0261231324718 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 50.1310022505785 36.3659894325471 63.89601506861 122 42.7134322932292 26.4792478318652 58.9476167545932 123 33.8597974522712 15.7862611517692 51.9333337527731 124 31.7957281947164 9.89408957299009 53.6973668164428 125 29.6683022081574 2.79624814561118 56.5403562707036 126 21.623822752465 -6.50999544322888 49.7576409481589 127 13.7602879246225 -14.5227010476891 42.0432768969341 128 7.12817126818914 -20.9065982331291 35.1629407695074 129 2.17906971793759 -29.7438008892835 34.1019403251587 130 -3.40015302711963 -39.887541806779 33.0872357525397 131 -10.4762434400666 -54.6994349640185 33.7469480838852 132 -17.6446353131815 -64.2947760881851 29.0055054618220

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/1kp8w1282256323.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/1kp8w1282256323.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/2kp8w1282256323.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/2kp8w1282256323.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/3i1e51282256323.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/20/t12822564946yjtsq0mnku42ff/3i1e51282256323.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

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=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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