IKO opgave 10 oe 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 12:42:09 +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/Jun/06/t1275828151dbcxz3l93p8wir7.htm/, Retrieved Sun, 06 Jun 2010 14:42:35 +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/Jun/06/t1275828151dbcxz3l93p8wir7.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 «

278,1 283,3 287 287,9 279,7 273,2 272,6 274,8 277,2 277,5 278,7 279 280,1 280,8 280,1 270,5 260 258,2 260,1 262,2 263,4 264,7 267,4 266,8 265,2 262,5 255 252,8 249,6 254,2 259,4 260,8 261,6 257,2 249,8 235,2 227,4 223,1 221,6 218,5 220,1 222,1 222,9 222,8 222,1 209 201,7 204,5 208,7 213 218,6 221,9 224,6 226,8 229,6 231,4 229,1 232,7 236,6 242,2 251,5 261,5 266,4 280,9 294,4 308,8 328,8 348,2 365,9 387,5 395,9 395,8

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 0.999924589277296 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 283.3 278.1 5.19999999999999 3 287 283.299607864242 3.70039213575802 4 287.9 286.999720950755 0.900279049245228 5 279.7 287.899932109306 -8.19993210930625 6 273.2 279.700618362806 -6.50061836280645 7 272.6 273.200490216329 -0.600490216328694 8 274.8 272.600045283401 2.19995471659877 9 277.2 274.799834099825 2.40016590017507 10 277.5 277.199819001755 0.300180998245196 11 278.7 277.499977363134 1.20002263686604 12 279 278.699909505426 0.300090494574306 13 280.1 278.999977369959 1.10002263004111 14 280.8 280.099917046498 0.700082953501521 15 280.1 280.799947206239 -0.699947206238505 16 270.5 280.100052783525 -9.60005278352469 17 260 270.500723946918 -10.5007239469184 18 258.2 260.000791867182 -1.80079186718177 19 260.1 258.200135799016 1.89986420098387 20 262.2 260.099856729868 2.10014327013238 21 263.4 262.199841626678 1.20015837332181 22 264.7 263.399909495190 1.30009050481033 23 267.4 264.699901959235 2.70009804076449 24 266.8 267.399796383655 -0.59979638365536 25 265.2 266.800045231079 -1.60004523107875 26 262.5 265.200120660567 -2.70012066056722 27 255 262.500203618050 -7.50020361805036 28 252.8 255.000565595775 -2.20056559577526 29 249.6 252.800165946242 -3.20016594624195 30 254.2 249.600241326827 4.59975867317323 31 259.4 254.199653128874 5.20034687112579 32 260.8 259.399607838084 1.40039216191593 33 261.6 260.799894395415 0.800105604585042 34 257.2 261.599939663458 -4.39993966345816 35 249.8 257.20033180263 -7.40033180262986 36 235.2 249.800558064369 -14.6005580643695 37 227.4 235.201101038635 -7.8011010386355 38 223.1 227.400588286667 -4.30058828666722 39 221.6 223.100324310471 -1.50032431047077 40 218.5 221.600113140541 -3.10011314054054 41 220.1 218.500233781772 1.59976621822761 42 222.1 220.099879360473 2.00012063952667 43 222.9 222.099849169457 0.800150830542918 44 222.8 222.899939660048 -0.0999396600475961 45 222.1 222.800007536522 -0.700007536522008 46 209 222.100052788074 -13.1000527880742 47 201.7 209.000987884448 -7.30098788444823 48 204.5 201.700550572773 2.79944942722722 49 208.7 204.499788891496 4.20021110850445 50 213 208.699683259045 4.3003167409552 51 218.6 212.999675710007 5.6003242899933 52 221.9 218.599577675498 3.30042232450211 53 224.6 221.899751112767 2.70024888723270 54 226.8 224.59979637228 2.20020362772007 55 229.6 226.799834081054 2.80016591894565 56 231.4 229.599788837464 1.80021116253565 57 229.1 231.399864244775 -2.29986424477525 58 232.7 229.100173434425 3.59982656557517 59 236.6 232.699728534477 3.90027146552293 60 242.2 236.59970587771 5.60029412228994 61 251.5 242.199577677773 9.30042232222712 62 261.5 251.499298648431 10.0007013515688 63 266.4 261.499245839884 4.90075416011643 64 280.9 266.399630430587 14.500369569413 65 294.4 280.898906516651 13.5010934833487 66 308.8 294.398981872783 14.4010181272169 67 328.8 308.798914008815 20.0010859911847 68 348.2 328.798491703651 19.4015082963494 69 365.9 348.198536918238 17.7014630817622 70 387.5 365.898665119876 21.6013348801239 71 395.9 387.498371027725 8.40162897227464 72 395.8 395.899366427087 -0.0993664270872614 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 395.800007493294 381.842329321405 409.757685665183 74 395.800007493294 376.061613980661 415.538401005928 75 395.800007493294 371.625815118592 419.974199867997 76 395.800007493294 367.886229972531 423.713785014058 77 395.800007493294 364.591573152747 427.008441833841 78 395.800007493294 361.612966490923 429.987048495665 79 395.800007493294 358.873849136279 432.726165850309 80 395.800007493294 356.324336890796 435.275678095792 81 395.800007493294 353.929779788797 437.670235197791 82 395.800007493294 351.664949245502 439.935065741086 83 395.800007493294 349.510799625309 442.08921536128 84 395.800007493294 347.452534306424 444.147480680164

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/1srf41275828126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/1srf41275828126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/2liw71275828126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/2liw71275828126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/3liw71275828126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275828151dbcxz3l93p8wir7/3liw71275828126.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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