exponential smoothing - nietwerkende werkzoekenden - Lize Geunes

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 07:48:47 -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/02/t1243950566idl0oshicz8ealm.htm/, Retrieved Tue, 02 Jun 2009 15:49:30 +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/02/t1243950566idl0oshicz8ealm.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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220206 220115 218444 214912 210705 209673 237041 242081 241878 242621 238545 240337 244752 244576 241572 240541 236089 236997 264579 270349 269645 267037 258113 262813 267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319

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 0.921339261357122 beta 0.180937138360347 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 244752 232009.034455128 12742.9655448717 14 244576 245522.595096673 -946.595096672943 15 241572 243428.082729499 -1856.08272949874 16 240541 242319.706374761 -1778.70637476142 17 236089 237906.726555531 -1817.72655553120 18 236997 238595.606067781 -1598.60606778093 19 264579 263190.541746734 1388.45825326623 20 270349 270640.247618376 -291.247618376219 21 269645 271309.905570763 -1664.90557076276 22 267037 271333.744620185 -4296.74462018523 23 258113 263303.480405773 -5190.48040577321 24 262813 259381.880936987 3431.11906301271 25 267413 267511.303588251 -98.3035882508848 26 267366 265663.007564142 1702.99243585835 27 264777 263925.961088967 851.038911032956 28 258863 263756.975839852 -4893.97583985189 29 254844 254390.50436265 453.495637350221 30 254868 255487.606934048 -619.606934048032 31 277267 279681.121890495 -2414.12189049466 32 285351 281322.951548248 4028.04845175165 33 286602 284411.85671985 2190.14328014990 34 283042 286970.898294348 -3928.89829434769 35 276687 278460.982126856 -1773.98212685587 36 277915 278186.602344273 -271.602344273007 37 277128 281830.95941776 -4702.95941775985 38 277103 274318.31169105 2784.68830895005 39 275037 272127.589579662 2909.41042033804 40 270150 272363.026264794 -2213.02626479388 41 267140 265294.051827205 1845.94817279465 42 264993 267228.589519252 -2235.58951925213 43 287259 289161.611821614 -1902.61182161386 44 291186 291236.266110164 -50.2661101644044 45 292300 289198.020074834 3101.97992516571 46 288186 291042.782580104 -2856.78258010407 47 281477 282795.820872853 -1318.82087285299 48 282656 282240.519614241 415.480385759322 49 280190 285465.421224797 -5275.4212247968 50 280408 277214.975969950 3193.02403005044 51 276836 274679.001830959 2156.99816904112 52 275216 272961.567922090 2254.43207791046 53 274352 270215.956550630 4136.04344936967 54 271311 274209.197696483 -2898.19769648334 55 289802 295717.271116954 -5915.27111695439 56 290726 293731.029192182 -3005.02919218160 57 292300 288216.247108030 4083.75289196969 58 278506 289658.346079567 -11152.3460795669 59 269826 271667.936697812 -1841.93669781188 60 265861 268458.487421693 -2597.48742169334 61 269034 265648.895426095 3385.10457390529 62 264176 264676.737756064 -500.737756063812 63 255198 256673.165612966 -1475.16561296556 64 253353 249028.547133586 4324.45286641447 65 246057 246094.824187623 -37.8241876228421 66 235372 242750.084191101 -7378.08419110082 67 258556 256207.405470787 2348.59452921333 68 260993 259755.601095853 1237.39890414698 69 254663 257106.067124817 -2443.06712481679 70 250643 248647.141275242 1995.85872475817 71 243422 243005.791154965 416.208845035406 72 247105 241696.609126891 5408.39087310899 73 248541 247947.539364303 593.460635697207 74 245039 244846.084858005 192.915141995181 75 237080 238269.005756521 -1189.00575652113 76 237085 232255.996601957 4829.00339804275 77 225554 230439.863514258 -4885.8635142576 78 226839 222238.721930589 4600.27806941132 79 247934 249681.810803709 -1747.81080370874 80 248333 250870.055160424 -2537.05516042383 81 246969 245325.877119436 1643.12288056378 82 245098 242534.490782082 2563.50921791792 83 246263 238940.115851961 7322.88414803939 84 255765 247186.620382074 8578.37961792576 85 264319 259307.49780461 5011.50219538985 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 264309.616669019 256899.23533014 271719.998007898 87 261478.499962085 250527.572899378 272429.427024793 88 261264.967743390 246899.083236489 275630.852250292 89 257661.107284032 239847.253046961 275474.961521103 90 258947.787527314 237597.395313867 280298.179740760 91 285126.324277284 260127.357876168 310125.290678400 92 291627.390747517 262857.392973076 320397.388521957 93 292937.033554246 260269.239797812 325604.827310679 94 292617.772331913 255924.225203949 329311.319459877 95 290522.163631672 249675.378244173 331368.949019171 96 294386.059999668 249259.9331474 339512.186851937 97 299158.206183333 249628.509089475 348687.90327719

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/1lav41243950525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/1lav41243950525.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/23mq81243950525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/23mq81243950525.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/3mru81243950525.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243950566idl0oshicz8ealm/3mru81243950525.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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=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')

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Software written by Ed van Stee & Patrick Wessa

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