*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: Thu, 03 Dec 2009 13:15:03 -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/03/t1259871436hmutih0prbl6nf8.htm/, Retrieved Thu, 03 Dec 2009 21:17:19 +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/03/t1259871436hmutih0prbl6nf8.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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1915 1843 1761 2858 3968 5061 4661 4269 3857 3568 3274 2987 1683 1381 1071 2772 4485 6181 5479 4782 4067 3489 2903 2330 1736 1483 1242 2334 3423 4523 3986 3462 2908 2575 2237 1904 1610 1251 941 2450 3946 5409 4741 4069 3539 3189 2960 2704 1697 1598 1456 2316 3083 4158 3469 2892 2578 2233 1947 2049

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.828031507927449 beta 0.0238508238386854 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1683 1608.82688568856 74.173114311443 14 1381 1357.91369803671 23.0863019632907 15 1071 1066.28848584284 4.71151415715826 16 2772 2785.53972128617 -13.5397212861740 17 4485 4545.20556285968 -60.2055628596772 18 6181 6316.13672702229 -135.136727022292 19 5479 4832.39132443641 646.60867556359 20 4782 5000.19699281017 -218.196992810166 21 4067 4452.10689138544 -385.106891385442 22 3489 3886.04616744914 -397.046167449143 23 2903 3260.85490757784 -357.854907577836 24 2330 2655.72885525292 -325.728855252919 25 1736 1322.58623241317 413.41376758683 26 1483 1344.55721732629 138.442782673713 27 1242 1126.73212815318 115.267871846817 28 2334 3177.97827150418 -843.97827150418 29 3423 4040.06744600806 -617.067446008059 30 4523 4918.78016910112 -395.780169101118 31 3986 3634.74365214425 351.256347855753 32 3462 3527.23052753161 -65.2305275316098 33 2908 3158.16172619785 -250.161726197848 34 2575 2744.05834623958 -169.058346239581 35 2237 2365.38877749005 -128.388777490051 36 1904 2004.33273938258 -100.332739382581 37 1610 1130.67522592317 479.32477407683 38 1251 1198.90329836119 52.0967016388136 39 941 955.488148912645 -14.4881489126451 40 2450 2261.01843060231 188.981569397691 41 3946 4061.70666127552 -115.706661275522 42 5409 5632.51938345435 -223.519383454351 43 4741 4463.70607781966 277.293922180342 44 4069 4153.60882164347 -84.608821643471 45 3539 3683.19537392962 -144.195373929622 46 3189 3339.77686084301 -150.776860843009 47 2960 2938.66957330701 21.3304266929872 48 2704 2641.60669293092 62.3933070690814 49 1697 1699.11320866254 -2.11320866254096 50 1598 1273.45633975121 324.543660248789 51 1456 1178.62199538218 277.378004617822 52 2316 3451.24944071099 -1135.24944071099 53 3083 4139.73061534856 -1056.73061534856 54 4158 4601.15720943110 -443.157209431104 55 3469 3504.3834670024 -35.3834670024021 56 2892 3008.05001865794 -116.050018657943 57 2578 2593.80801454288 -15.8080145428780 58 2233 2395.13960123425 -162.139601234248 59 1947 2066.11658394733 -119.116583947327 60 2049 1742.94071949305 306.059280506953 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 1244.68194867836 561.971603604106 1927.39229375260 62 960.496174209674 143.389829012212 1777.60251940714 63 724.153742216713 -158.87865004749 1607.18613448091 64 1560.72603964466 -331.275912624212 3452.72799191354 65 2611.86068960467 -649.329843687843 5873.05122289719 66 3815.91764761312 -1095.80710359984 8727.64239882609 67 3207.60637079217 -1076.64551685901 7491.85825844334 68 2760.52415725046 -1072.73212523263 6593.78043973356 69 2473.99289193048 -1101.44868362714 6049.4344674881 70 2271.16634397577 -1147.36078808421 5689.69347603576 71 2084.18226056431 -1186.62190441156 5354.98642554018 72 1922.31883787362 -1151.61036806363 4996.24804381086

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/1n5r81259871301.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/1n5r81259871301.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/200tf1259871301.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/200tf1259871301.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/3ug091259871301.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259871436hmutih0prbl6nf8/3ug091259871301.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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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