Opgave 10, oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 06:04:30 -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/03/t1244030698c6kfh8rfemsp72j.htm/, Retrieved Wed, 03 Jun 2009 14:05:02 +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/03/t1244030698c6kfh8rfemsp72j.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:

» Textbox « » Textfile « » CSV «

41 39 50 40 43 38 44 35 39 35 29 49 50 59 63 32 47 53 60 57 52 70 90 74 62 55 84 94 70 108 139 120 97 126 149 158 124 140 109 114 77 120 133 110 92 97 78 99 107 112 90 98 125 155 190 236 189 174 178 136 161 171 149 184 155 276 224 213 279 268 287 238 213 257 293 212 246 353 339 308 247 257 322 298 273 312 249 286 279 309 401 309 328 353 354 327 324 285 243 241 287 355 460 364 487 452 391 500 451 375 372 302 316 398 394 431 431

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 0.211758486366268 beta 0.00338345770218744 gamma 0.436282320230838 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50 44.9818781584533 5.01812184154671 14 59 54.2945300365497 4.70546996345035 15 63 59.1229092170687 3.87709078293130 16 32 30.1484853928934 1.85151460710664 17 47 42.7937050193243 4.20629498067568 18 53 47.5282918055132 5.47170819448682 19 60 59.2660501556075 0.733949844392491 20 57 47.1088182790875 9.8911817209125 21 52 54.3911775331105 -2.3911775331105 22 70 49.2965297010707 20.7034702989293 23 90 45.6362081328332 44.3637918671668 24 74 92.9972836592548 -18.9972836592548 25 62 93.2273628458895 -31.2273628458895 26 55 99.8920133561325 -44.8920133561325 27 84 94.9056693010717 -10.9056693010717 28 94 46.0447786844064 47.9552213155936 29 70 78.7271848301798 -8.72718483017984 30 108 83.1872335539068 24.8127664460932 31 139 102.997140969116 36.0028590308844 32 120 92.3493559172146 27.6506440827854 33 97 98.968774832317 -1.96877483231704 34 126 102.666597836476 23.3334021635236 35 149 102.287708811369 46.7122911886312 36 158 136.701114604532 21.2988853954675 37 124 138.942725926159 -14.9427259261588 38 140 147.113941927190 -7.11394192719041 39 109 175.358308233225 -66.3583082332254 40 114 107.241430811878 6.75856918812161 41 77 112.530655571416 -35.5306555714160 42 120 129.048900838430 -9.04890083842955 43 133 149.610080578132 -16.6100805781318 44 110 120.021859777717 -10.0218597777165 45 92 107.427038899669 -15.4270388996686 46 97 117.269087621380 -20.2690876213804 47 78 114.214210369593 -36.2142103695933 48 99 119.609962720668 -20.6099627206684 49 107 103.914901838829 3.08509816117078 50 112 115.955690292417 -3.95569029241652 51 90 121.240818319716 -31.2408183197158 52 98 90.7802058652143 7.21979413478573 53 125 82.7952557819846 42.2047442180154 54 155 124.409473323439 30.5905266765607 55 190 151.575694672860 38.4243053271405 56 236 132.351631649902 103.648368350098 57 189 137.070633005233 51.9293669947672 58 174 164.239352137576 9.76064786242446 59 178 157.634531719911 20.3654682800888 60 136 192.326069971329 -56.326069971329 61 161 174.29687080369 -13.2968708036901 62 171 185.236946979371 -14.2369469793711 63 149 175.285000998686 -26.2850009986861 64 184 151.636388399876 32.3636116001242 65 155 159.634391727341 -4.63439172734067 66 276 200.047448093627 75.9525519063732 67 224 250.039308392898 -26.0393083928978 68 213 229.784089747381 -16.7840897473808 69 279 182.691163452238 96.3088365477616 70 268 204.792241682465 63.207758317535 71 287 211.141912861792 75.8580871382076 72 238 230.478008948747 7.52199105125348 73 213 243.992291100576 -30.9922911005764 74 257 255.905751633004 1.09424836699591 75 293 239.205687846915 53.794312153085 76 212 252.491739446472 -40.4917394464719 77 246 226.800650064151 19.1993499358493 78 353 328.91578294615 24.0842170538502 79 339 331.575864584611 7.42413541538883 80 308 316.113103317822 -8.1131033178217 81 247 302.478464059447 -55.4784640594471 82 257 276.864482290498 -19.8644822904984 83 322 267.299678017872 54.7003219821281 84 298 256.431691255844 41.5683087441556 85 273 263.221976885451 9.77802311454889 86 312 299.571853183095 12.4281468169047 87 249 302.366843781185 -53.3668437811846 88 286 257.377571209584 28.6224287904157 89 279 267.020914241607 11.9790857583935 90 309 382.363034867825 -73.3630348678246 91 401 357.885231344662 43.1147686553378 92 309 342.348465368962 -33.3484653689624 93 328 303.958862667521 24.0411373324789 94 353 306.884468764524 46.1155312354764 95 354 339.611870038297 14.388129961703 96 327 310.865213306325 16.1347866936754 97 324 299.525139483759 24.4748605162409 98 285 344.375760255379 -59.3757602553791 99 243 306.569038451894 -63.5690384518942 100 241 286.829349354318 -45.829349354318 101 287 274.833022813212 12.1669771867881 102 355 360.817478409014 -5.81747840901437 103 460 391.794319877253 68.2056801227468 104 364 351.619034734239 12.380965265761 105 487 341.247215884008 145.752784115992 106 452 377.665676049676 74.334323950324 107 391 407.361668786917 -16.3616687869167 108 500 367.373824315778 132.626175684222 109 451 380.32426503703 70.6757349629697 110 375 407.70415901952 -32.70415901952 111 372 364.878955872964 7.12104412703633 112 302 365.085961335209 -63.085961335209 113 316 375.101472657518 -59.1014726575185 114 398 461.649595401111 -63.649595401111 115 394 519.019844851991 -125.019844851991 116 431 407.677597645104 23.3224023548963 117 431 445.427876451213 -14.4278764512130 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 118 421.252994457504 374.109634423978 468.396354491029 119 403.781873008052 353.602308462305 453.961437553798 120 415.312127710863 361.700106392753 468.924149028973 121 380.095834046952 324.996981426188 435.194686667717 122 358.948344719755 302.095734876109 415.800954563402 123 338.45747626022 280.121173973430 396.79377854701 124 314.335338085329 255.049355209065 373.621320961593 125 337.195230666006 273.360929072824 401.029532259187 126 432.526150001749 356.43779404065 508.614505962848 127 480.543647622941 396.829771857601 564.257523388282 128 444.109488595475 363.045642774212 525.173334416738 129 464.870756492779 386.981794380782 542.759718604775

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/11mb81244030667.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/11mb81244030667.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/2zort1244030667.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/2zort1244030667.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/3n81h1244030667.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244030698c6kfh8rfemsp72j/3n81h1244030667.ps (open in new window)

Parameters (Session):

par1 = 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=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')

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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