*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 21:01:19 +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/02/t1275512719nv6bzfqlpcs1z30.htm/, Retrieved Wed, 02 Jun 2010 23:05:20 +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/02/t1275512719nv6bzfqlpcs1z30.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

225 243 270 289 273 274 220 271 288 276 266 239 201 242 239 273 280 294 212 264 272 262 238 227 250 245 270 288 298 281 218 284 281 277 276 222 255 267 261 263 264 278 248 320 305 301 274 220 235 252 272 280 305 299 246 307 325 302 274 251 272 253 292 288 258 295 231 250 268

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.34126575693962 beta 0 gamma 0.660091540095026 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 201 201.63706732081 -0.637067320809876 14 242 242.488883213482 -0.488883213482097 15 239 239.61359667665 -0.613596676650189 16 273 274.115023149593 -1.11502314959273 17 280 281.985390904853 -1.98539090485286 18 294 296.581420610356 -2.58142061035574 19 212 212.790148615504 -0.790148615504137 20 264 262.165822291584 1.83417770841567 21 272 280.002229273858 -8.00222927385767 22 262 267.057972290363 -5.05797229036318 23 238 255.423546961307 -17.4235469613072 24 227 222.572218502482 4.42778149751754 25 250 187.327211212702 62.6727887872979 26 245 251.420246684895 -6.4202466848952 27 270 246.402763641842 23.5972363581584 28 288 291.201448650303 -3.20144865030318 29 298 298.508750191992 -0.508750191991851 30 281 314.351749950383 -33.3517499503829 31 218 218.513780594727 -0.513780594726995 32 284 270.617360098391 13.3826399016089 33 281 288.682131665687 -7.68213166568745 34 277 276.742961746295 0.257038253705332 35 276 260.593651499156 15.4063485008438 36 222 246.770044116115 -24.7700441161146 37 255 223.350988685109 31.6490113148906 38 267 246.686925592339 20.3130744076611 39 261 263.826998694924 -2.8269986949245 40 263 287.769491070318 -24.7694910703182 41 264 288.552323159868 -24.5523231598683 42 278 281.249581308694 -3.24958130869396 43 248 211.973174249989 36.0268257500108 44 320 284.15467305655 35.8453269434504 45 305 300.969337056063 4.03066294393693 46 301 296.120134937481 4.8798650625194 47 274 287.31717017368 -13.3171701736804 48 220 244.475945031834 -24.475945031834 49 235 245.414214163067 -10.4142141630666 50 252 249.029859545349 2.97014045465119 51 272 250.148858136057 21.8511418639427 52 280 272.404406854553 7.59559314544714 53 305 284.240357765222 20.7596422347779 54 299 302.553013704055 -3.55301370405482 55 246 245.225255649056 0.774744350943848 56 307 306.04115163179 0.958848368209772 57 325 297.26217207135 27.7378279286503 58 302 300.816047046777 1.18395295322267 59 274 282.668197088828 -8.66819708882787 60 251 235.76162863253 15.2383713674699 61 272 257.394589066866 14.6054109331338 62 253 276.799370819002 -23.7993708190017 63 292 277.31708628611 14.6829137138899 64 288 291.422901204502 -3.42290120450195 65 258 305.667026345426 -47.6670263454264 66 295 290.000504536484 4.9994954635165 67 231 238.92048890566 -7.92048890565954 68 250 294.450211543451 -44.4502115434515 69 268 281.186686679723 -13.1866866797228 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 70 261.441490444896 232.052786489386 290.830194400405 71 241.534605288313 209.801421745394 273.267788831233 72 211.969218632856 178.743330365976 245.195106899736 73 225.611899135989 189.176350181303 262.047448090675 74 223.339726755872 184.800981073848 261.878472437896 75 245.088421844246 202.445563513779 287.731280174714 76 246.020424798304 201.298196593896 290.742653002711 77 241.671118341207 195.538420324883 287.80381635753 78 262.727368689373 212.084006447435 313.370730931311 79 210.418487076428 164.937932987881 255.899041164974 80 247.6861486502 195.009494059684 300.362803240716 81 262.331946860743 192.501922094577 332.161971626909

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/1j6wp1275512475.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/1j6wp1275512475.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/2uxea1275512475.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/2uxea1275512475.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/3uxea1275512475.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275512719nv6bzfqlpcs1z30/3uxea1275512475.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=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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