*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, 09 Dec 2009 09:18:05 -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/09/t126037558721tbq7xqzbh7b9k.htm/, Retrieved Wed, 09 Dec 2009 17:19:52 +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/09/t126037558721tbq7xqzbh7b9k.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:

» Textbox « » Textfile « » CSV «

153.4 145 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179 190.6 190 181.6 174.8 180.5 196.8 193.8 197 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191 159.7 163.4 157.6 166.2 176.7 198.3 226.2 216.2 235.9 226.9

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 181.6 162.668205537299 18.9317944627013 14 174.8 173.965461899269 0.834538100731436 15 180.5 179.809458103709 0.690541896291109 16 196.8 196.461557207486 0.33844279251403 17 193.8 193.754362177556 0.0456378224440641 18 197 198.431007856160 -1.43100785615954 19 216.3 210.589156655935 5.71084334406476 20 221.4 207.156661095842 14.2433389041580 21 217.9 238.696205080358 -20.7962050803579 22 229.7 222.840359127471 6.85964087252867 23 227.4 243.282502753135 -15.8825027531354 24 204.2 226.850408634663 -22.6504086346629 25 196.6 195.395451984539 1.20454801546083 26 198.8 188.059676843995 10.7403231560053 27 207.5 204.035532679675 3.46446732032513 28 190.7 225.311654618064 -34.6116546180635 29 201.6 187.85645276537 13.7435472346299 30 210.5 206.276744019244 4.22325598075636 31 223.5 224.768855491123 -1.26885549112251 32 223.8 213.937240128136 9.86275987186434 33 231.2 241.243919798407 -10.0439197984070 34 244 236.216642765629 7.78335723437115 35 234.7 258.18858828975 -23.4885882897499 36 250.2 234.011617482140 16.1883825178604 37 265.7 238.613341509980 27.0866584900195 38 287.6 252.9870270227 34.6129729773003 39 283.3 293.672008610749 -10.3720086107489 40 295.4 306.305631792944 -10.9056317929442 41 312.3 289.087783167969 23.2122168320309 42 333.8 317.625845718399 16.1741542816010 43 347.7 354.276771519166 -6.57677151916602 44 383.2 330.902228435202 52.2977715647977 45 407.1 410.454638988832 -3.35463898883216 46 413.6 413.125536897352 0.474463102648144 47 362.7 434.976847521205 -72.276847521205 48 321.9 359.57801919132 -37.6780191913198 49 239.4 305.976878009418 -66.5768780094183 50 191 228.275170152947 -37.2751701529466 51 159.7 196.162058442486 -36.4620584424860 52 163.4 174.236296980078 -10.8362969800780 53 157.6 161.46089096985 -3.86089096985009 54 166.2 162.018745150564 4.18125484943599 55 176.7 178.238436350471 -1.53843635047102 56 198.3 169.863476418226 28.4365235817735 57 226.2 214.174450919136 12.0255490808643 58 216.2 231.187964706171 -14.9879647061711 59 235.9 229.210324099688 6.68967590031178 60 226.9 235.188802498163 -8.28880249816314 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 216.722540946007 171.448391740376 261.996690151638 62 206.967104665800 144.842869855374 269.091339476225 63 212.279569625649 134.934748658532 289.624390592766 64 230.418730517346 136.185577206183 324.651883828508 65 226.259317447063 124.519414894416 327.999219999709 66 231.080654102755 119.176673815234 342.984634390277 67 246.38570563988 120.429521550080 372.34188972968 68 235.489786767166 108.524497015116 362.455076519216 69 253.653187214058 111.472588806964 395.833785621153 70 258.798612747275 108.806510731671 408.79071476288 71 273.614419578849 110.842018183598 436.3868209741 72 272.186177178369 111.950389069417 432.421965287321

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/19slr1260375482.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/19slr1260375482.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/2km9i1260375482.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/2km9i1260375482.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/3l1521260375482.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t126037558721tbq7xqzbh7b9k/3l1521260375482.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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