*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 12:53:20 -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/t1259956441at10fxedn6gf5un.htm/, Retrieved Fri, 04 Dec 2009 20:54:05 +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/t1259956441at10fxedn6gf5un.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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5560 3922 3759 4138 4634 3996 4308 4143 4429 5219 4929 5755 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5526 4247 3830 4394 4826 4409 4569 4106 4794 3914 3793 4405 4022 4100 4788 3163 3585 3903 4178 3863 4187

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 0.277254341489538 beta 0.097258390234304 gamma 0.452433755682275 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5592 5238.68248791591 353.31751208409 14 4163 3935.51659519542 227.483404804584 15 4962 4760.32445506898 201.675544931019 16 5208 5082.53187493351 125.468125066493 17 4755 4723.33769533325 31.6623046667464 18 4491 4563.81926664071 -72.8192666407149 19 5732 5034.31493456657 697.685065433434 20 5731 5114.2942342393 616.705765760701 21 5040 5699.13295441262 -659.132954412617 22 6102 6490.97195685918 -388.97195685918 23 4904 6068.89264576003 -1164.89264576003 24 5369 6756.14632973248 -1387.14632973248 25 5578 6266.3255281321 -688.3255281321 26 4619 4415.46618587403 203.533814125966 27 4731 5237.68846193254 -506.688461932541 28 5011 5271.06423036057 -260.064230360566 29 5299 4694.2415269454 604.758473054599 30 4146 4595.25595490521 -449.255954905211 31 4625 5121.12484018266 -496.124840182661 32 4736 4753.97026089655 -17.9702608965536 33 4219 4636.08973084054 -417.089730840545 34 5116 5308.43775572016 -192.437755720164 35 4205 4660.57688175995 -455.576881759947 36 4121 5202.5094190291 -1081.50941902910 37 5103 4897.60912864472 205.390871355279 38 4300 3732.88160090191 567.118399098094 39 4578 4286.02217213461 291.977827865392 40 3809 4550.7109470601 -741.710947060098 41 5526 4099.02790827187 1426.97209172813 42 4247 3922.99543678625 324.004563213745 43 3830 4590.97799967912 -760.977999679119 44 4394 4298.01757331991 95.9824266800888 45 4826 4087.762805934 738.237194066002 46 4409 5158.0265806207 -749.0265806207 47 4569 4303.69111136198 265.308888638021 48 4106 4847.15931538226 -741.159315382262 49 4794 5106.19081958986 -312.190819589859 50 3914 3929.44190868129 -15.4419086812909 51 3793 4220.95165934588 -427.951659345876 52 4405 3932.87097618722 472.129023812784 53 4022 4499.90741280991 -477.907412809911 54 4100 3513.95765222796 586.042347772044 55 4788 3841.21203685334 946.787963146664 56 3163 4322.05319388231 -1159.05319388231 57 3585 3952.21458139702 -367.214581397021 58 3903 4118.40463904438 -215.404639044376 59 4178 3753.28354416713 424.716455832868 60 3863 3955.73717859487 -92.7371785948667 61 4187 4453.2216652102 -266.221665210201 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 3482.54353582633 2780.16749069576 4184.9195809569 63 3609.23629718211 2815.16058797161 4403.31200639261 64 3716.55664392634 2819.30773568077 4613.80555217191 65 3807.59079318825 2797.20921579116 4817.97237058534 66 3339.80668718432 2302.33546993931 4377.27790442934 67 3546.50581583174 2355.94078585877 4737.0708458047 68 3105.40420211295 1910.49379467755 4300.31460954835 69 3267.47060099993 1907.43175087806 4627.5094511218 70 3537.37208247747 1955.54069517085 5119.2034697841 71 3446.49895045390 1762.84219546465 5130.15570544316 72 3360.57234025523 1573.34092155564 5147.80375895481 73 3748.96359391127 1739.60299337568 5758.32419444687

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/1d3sz1259956399.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/1d3sz1259956399.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/222b81259956399.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/222b81259956399.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/33h2a1259956399.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956441at10fxedn6gf5un/33h2a1259956399.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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