Exponential smoothing

*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: Fri, 04 Dec 2009 09:17:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f.htm/, Retrieved Fri, 04 Dec 2009 17:18:36 +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/2009/Dec/04/t1259943512us42vfa8d2o431f.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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462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441

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 0.425497132234063 beta 0.750351434132633 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 465 463.162941711369 1.83705828863145 14 459 458.438603676833 0.56139632316706 15 465 465.2984471025 -0.298447102499665 16 468 468.830611719609 -0.83061171960918 17 467 467.909466193403 -0.909466193403148 18 463 463.825386794596 -0.825386794596454 19 460 460.419032995802 -0.419032995802013 20 462 459.016008640727 2.98399135927286 21 461 461.993485896885 -0.99348589688526 22 476 478.029037775497 -2.02903777549699 23 476 476.781658147538 -0.781658147537769 24 471 475.06452024124 -4.06452024123956 25 453 466.714795056054 -13.7147950560544 26 443 448.038636565858 -5.0386365658581 27 442 443.333552989163 -1.33355298916308 28 444 437.088269004634 6.91173099536582 29 438 433.068855338723 4.9311446612769 30 427 427.274180244202 -0.274180244201943 31 424 420.249779292069 3.75022070793068 32 416 419.523401440320 -3.52340144031962 33 406 412.541952806296 -6.54195280629597 34 431 416.884948656035 14.1150513439655 35 434 421.294446197908 12.7055538020916 36 418 426.133221355773 -8.13322135577312 37 412 412.579570703811 -0.579570703811328 38 404 409.810577625581 -5.81057762558117 39 409 411.315704326062 -2.31570432606202 40 412 413.593992012247 -1.59399201224704 41 406 406.958288904532 -0.958288904532367 42 398 396.251196617057 1.74880338294253 43 397 393.162960410734 3.837039589266 44 385 389.289314676407 -4.28931467640746 45 390 380.944814075183 9.05518592481712 46 413 408.155227355912 4.84477264408798 47 413 410.499978301678 2.50002169832152 48 401 399.192627587688 1.80737241231230 49 397 396.994857742518 0.00514225748213448 50 397 394.338840993935 2.66115900606525 51 409 406.784928200258 2.21507179974157 52 419 418.453272028706 0.546727971294331 53 424 420.779974426139 3.22002557386071 54 428 422.158512469919 5.84148753008111 55 430 432.323650740407 -2.32365074040723 56 424 428.580034262214 -4.58003426221427 57 433 436.350283797238 -3.35028379723821 58 456 462.684911396768 -6.68491139676786 59 459 459.205190194173 -0.205190194172587 60 446 444.533659983181 1.46634001681929 61 441 440.164665677983 0.835334322016934 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 438.977121235833 429.358138622567 448.596103849099 63 449.959818637493 437.879824477006 462.039812797979 64 458.672292641558 442.625022915679 474.719562367438 65 460.438380994200 439.448550022769 481.42821196563 66 458.801946609596 432.220326222380 485.383566996812 67 456.844595561333 424.113858256671 489.575332865995 68 448.321099290396 409.504376041661 487.13782253913 69 456.661703837808 409.906279973285 503.417127702331 70 482.273770641975 424.887167385101 539.660373898848 71 486.148892116373 419.772623285923 552.525160946822 72 472.372587312214 399.216318720857 545.52885590357 73 466.855442403412 386.159178550149 547.551706256674

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/1ul5n1259943472.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/1ul5n1259943472.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/237nt1259943472.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/237nt1259943472.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/3dwiy1259943472.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943512us42vfa8d2o431f/3dwiy1259943472.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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