*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 29 Dec 2010 09:53:55 +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/Dec/29/t1293616307imej6mbgxlhl2hc.htm/, Retrieved Wed, 29 Dec 2010 10:51:50 +0100

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/Dec/29/t1293616307imej6mbgxlhl2hc.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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548604 563668 586111 604378 600991 544686 537034 551531 563250 574761 580112 575093 557560 564478 580523 596594 586570 536214 523597 536535 536322 532638 528222 516141 501866 506174 517945 533590 528379 477580 469357 490243 492622 507561 516922 514258 509846 527070 541657 564591 555362 498662 511038 525919 531673 548854 560576 557274 565742

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.538874295124119 beta 0.428829606945443 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 557560 561909.007211539 -4349.00721153873 14 564478 565213.514458388 -735.514458387857 15 580523 579984.398521435 538.601478564553 16 596594 596722.625437075 -128.625437075272 17 586570 588016.660810633 -1446.66081063310 18 536214 538635.347156418 -2421.34715641825 19 523597 517241.262466417 6355.73753358313 20 536535 532801.306979333 3733.69302066742 21 536322 545639.200496777 -9317.20049677696 22 532638 549441.318676276 -16803.3186762757 23 528222 539534.40273163 -11312.4027316298 24 516141 519630.937475008 -3489.93747500784 25 501866 488575.885572277 13290.1144277233 26 506174 498028.868496813 8145.1315031866 27 517945 515201.950358506 2743.04964149435 28 533590 530358.956058257 3231.04394174251 29 528379 521170.55477107 7208.44522892957 30 477580 476318.773578214 1261.22642178612 31 469357 462122.432161098 7234.56783890235 32 490243 478316.008001068 11926.9919989324 33 492622 492813.352208155 -191.352208155207 34 507561 503452.357832821 4108.64216717862 35 516922 517550.052181178 -628.052181177773 36 514258 519683.934091286 -5425.93409128557 37 509846 507548.64186149 2297.35813851003 38 527070 518390.4684758 8679.53152419964 39 541657 543169.019293722 -1512.01929372235 40 564591 565083.354085944 -492.35408594436 41 555362 563687.41856105 -8325.4185610502 42 498662 512097.602450021 -13435.6024500211 43 511038 493714.939046227 17323.0609537727 44 525919 520819.003916929 5099.99608307052 45 531673 527782.019441054 3890.98055894650 46 548854 545279.738035707 3574.26196429273 47 560576 559457.780565164 1118.21943483583 48 557274 563276.317756909 -6002.31775690883 49 565742 557214.70306746 8527.29693253944 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 50 578619.182044869 564333.878843265 592904.485246473 51 596277.772930674 578248.623997473 614306.921863875 52 622083.297806153 599071.415097421 645095.180514884 53 620060.635547424 591089.02330541 649032.247789437 54 575244.601477429 539519.711746819 610969.491208038 55 586034.283926987 542882.437366341 629186.130487634 56 601912.557934125 550740.383008735 653084.732859515 57 608136.805448691 548407.487304475 667866.123592907 58 625059.576249047 556278.20839093 693840.944107163 59 637020.886008914 558725.026177877 715316.745839952 60 637536.866208807 549290.157616237 725783.574801377 61 643380.257646964 544767.930215956 741992.585077973

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/1bwa21293616431.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/1bwa21293616431.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/24ns51293616431.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/24ns51293616431.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/34ns51293616431.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616307imej6mbgxlhl2hc/34ns51293616431.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=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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