*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 11:06:24 -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/Aug/18/t1250615254x9hwel9591pflhe.htm/, Retrieved Tue, 18 Aug 2009 19:07:34 +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/Aug/18/t1250615254x9hwel9591pflhe.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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6430 5124 4836 4629 4597 4490 4517 4560 4135 4559 4739 4886 5605 4616 4997 4607 4882 4555 4462 4476 4277 4369 4492 5183 6039 4923 4953 4892 4614 4363 4675 4556 4217 4664 4601 5428 5607 4869 5174 5031 4671 4491 4504 4615 4582 4800 4775 5791 5818 4714 4915 4598 4407 4383 4412 4274 4236 4637 4534 5271 5467 5204 5752 4724 4623 4451 4138 4140 4169 4603 4434 5185

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.82052932810292 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 5124 6430 -1306 3 4836 5358.38869749759 -522.388697497587 4 4629 4929.75345053133 -300.753450531332 5 4597 4682.97642384222 -85.976423842223 6 4490 4612.43024655427 -122.430246554272 7 4517 4511.97263860962 5.02736139037916 8 4560 4516.0977360734 43.9022639266004 9 4135 4552.12083119529 -417.120831195291 10 4559 4209.86095583689 349.139044163113 11 4739 4496.33978115854 242.660218841458 12 4886 4695.44960748183 190.550392518169 13 5605 4851.80179302451 753.198206975489 14 4616 5469.82301172243 -853.823011722433 15 4997 4769.23618959501 227.763810404987 16 4607 4956.12307591278 -349.123075912778 17 4882 4669.65735300884 212.342646991158 18 4555 4843.89072247209 -288.890722472092 19 4462 4606.8474120669 -144.847412066899 20 4476 4487.9958623662 -11.9958623661996 21 4277 4478.15290547885 -201.152905478847 22 4369 4313.10104710034 55.8989528996617 23 4492 4358.96777736475 133.032222635245 24 5183 4468.12461761969 714.875382380309 25 6039 5054.70083480152 984.299165198476 26 4923 5862.3471674741 -939.347167474095 27 4953 5091.58526729119 -138.585267291194 28 4892 4977.87199103579 -85.8719910357868 29 4614 4907.41150392833 -293.411503928332 30 4363 4666.65875975235 -303.658759752350 31 4675 4417.49784164019 257.502158359812 32 4556 4628.78591462422 -72.7859146242163 33 4217 4569.06293700225 -352.062937002252 34 4664 4280.18497185385 383.815028146147 35 4601 4595.11645901441 5.88354098558557 36 5428 4599.94407694618 828.055923053817 37 5607 5279.38824712117 327.611752878825 38 4869 5548.20329858946 -679.203298589458 39 5174 4990.89707235256 183.102927647437 40 5031 5141.13839454879 -110.138394548792 41 4671 5050.76661167134 -379.766611671337 42 4491 4739.15696896073 -248.156968960732 43 4504 4535.53689795533 -31.536897955325 44 4615 4509.65994826559 105.340051734408 45 4582 4596.09455013755 -14.0945501375527 46 4800 4584.52955838327 215.470441616726 47 4775 4761.32937506909 13.6706249309145 48 5791 4772.5465237584 1018.45347624160 49 5818 5608.217470323 209.782529676997 50 4714 5780.3501884466 -1066.3501884466 51 4915 4905.37858479809 9.62141520191108 52 4598 4913.27323814911 -315.273238149112 53 4407 4654.58229988179 -247.582299881789 54 4383 4451.43376170961 -68.4337617096089 55 4412 4395.28185319447 16.7181468055314 56 4274 4408.99958295994 -134.999582959937 57 4236 4298.22846585965 -62.2284658596454 58 4637 4247.16818457896 389.831815421045 59 4534 4567.03662215953 -33.0366221595268 60 5271 4539.92910477618 731.07089522382 61 5467 5139.79421522978 327.205784770219 62 5204 5408.27615795868 -204.276157958678 63 5752 5240.6615793214 511.338420678602 64 4724 5660.22975007402 -936.22975007402 65 4623 4892.02578229582 -269.025782295819 66 4451 4671.28223790627 -220.282237906268 67 4138 4490.53420124403 -352.534201244031 68 4140 4201.26954996397 -61.2695499639667 69 4169 4150.99608729886 18.0039127011351 70 4603 4165.76882569075 437.231174309249 71 4434 4524.52982737237 -90.5298273723702 72 5185 4450.24744894525 734.752551054754 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 5053.13346598411 4177.56582993928 5928.70110202894 74 5053.13346598411 3920.5440415718 6185.72289039642 75 5053.13346598411 3711.90308931794 6394.36384265028 76 5053.13346598411 3531.60823047418 6574.65870149404 77 5053.13346598411 3370.52264904068 6735.74428292754 78 5053.13346598411 3223.56540758986 6882.70152437836 79 5053.13346598411 3087.56499877214 7018.70193319607 80 5053.13346598411 2960.38419330487 7145.88273866335 81 5053.13346598411 2840.50163097383 7265.76530099439 82 5053.13346598411 2726.78874597754 7379.47818599068 83 5053.13346598411 2618.38093742933 7487.88599453889 84 5053.13346598411 2514.59845651401 7591.66847545421

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/1zd971250615179.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/1zd971250615179.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/24iso1250615179.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/24iso1250615179.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/3ynyc1250615179.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250615254x9hwel9591pflhe/3ynyc1250615179.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=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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