w

*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 10:24:44 -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/t1259861166kf3snmj64ndsz6w.htm/, Retrieved Thu, 03 Dec 2009 18:26:10 +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/t1259861166kf3snmj64ndsz6w.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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13132.1 17665.9 16913 17318.8 16224.2 15469.6 16557.5 19414.8 17335 16525.2 18160.4 15553.8 15262.2 18581 17564.1 18948.6 17187.8 17564.8 17668.4 20811.7 17257.8 18984.2 20532.6 17082.3 16894.9 20274.9 20078.6 19900.9 17012.2 19642.9 19024 21691 18835.9 19873.4 21468.2 19406.8 18385.3 20739.3 22268.3 21569 17514.8 21124.7 21251 21393 22145.2 20310.5 23466.9 21264.6 18388.1 22635.4 22014.3 18422.7 16120.2 16037.7 16410.7 17749.8 16349.8 15662.3 17782.3 16398.9

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.311491073238867 beta 0.198311700434253 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 15262.2 14642.7843279036 619.415672096362 14 18581 18118.4834432848 462.516556715174 15 17564.1 17390.8746132434 173.225386756629 16 18948.6 18920.8218426668 27.7781573331667 17 17187.8 17163.9949958722 23.8050041278475 18 17564.8 17580.668405127 -15.8684051270102 19 17668.4 18022.9436502772 -354.543650277174 20 20811.7 21044.3377955138 -232.637795513809 21 17257.8 18816.9020020803 -1559.10200208033 22 18984.2 17441.4214663555 1542.77853364446 23 20532.6 19745.2406121274 787.359387872613 24 17082.3 17184.1730324847 -101.873032484731 25 16894.9 17365.1292307161 -470.229230716148 26 20274.9 20793.3156484679 -518.415648467897 27 20078.6 19381.2679325466 697.33206745343 28 19900.9 21100.5621325104 -1199.66213251041 29 17012.2 18698.9432523858 -1686.74325238578 30 19642.9 18382.5358630304 1260.36413696965 31 19024 18884.0072523413 139.992747658656 32 21691 22270.1591755163 -579.159175516299 33 18835.9 18701.2075968680 134.692403132041 34 19873.4 20066.6909084720 -193.290908472030 35 21468.2 21251.2814731504 216.918526849619 36 19406.8 17639.6546540046 1767.14534599536 37 18385.3 18125.0818283013 260.218171698732 38 20739.3 22050.6191387497 -1311.31913874966 39 22268.3 21181.0612114590 1087.23878854096 40 21569 21719.030309965 -150.030309964983 41 17514.8 19123.4283381395 -1608.62833813954 42 21124.7 21129.4605710907 -4.76057109073736 43 21251 20404.8071634457 846.192836554284 44 21393 23794.4895257723 -2401.48952577232 45 22145.2 19905.6647340366 2239.53526596338 46 20310.5 21871.8211575444 -1561.32115754439 47 23466.9 23013.3021334836 453.597866516368 48 21264.6 20296.2891951033 968.310804896715 49 18388.1 19366.8994649676 -978.799464967553 50 22635.4 21757.2621186045 878.13788139549 51 22014.3 23261.6939461822 -1247.39394618223 52 18422.7 22044.6205255027 -3621.92052550270 53 16120.2 17143.7070166730 -1023.50701667302 54 16037.7 19969.4835900108 -3931.78359001076 55 16410.7 18061.4499175978 -1650.74991759779 56 17749.8 17518.9750607891 230.824939210892 57 16349.8 17001.9720051595 -652.172005159511 58 15662.3 15064.6069679350 597.693032065039 59 17782.3 16842.0211896562 940.278810343767 60 16398.9 14736.5583475352 1662.34165246485 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 12962.318981157 10473.9966432103 15450.6413191037 62 15277.3509126681 12546.4029491879 18008.2988761483 63 14602.8882141092 11655.1143141912 17550.6621140273 64 12477.5640325729 9409.06376016824 15546.0643049776 65 10882.9735733212 7679.75340311765 14086.1937435248 66 11318.6247551700 7691.90763956933 14945.3418707707 67 11853.1013534477 7676.41975220837 16029.7829546871 68 12776.9950409588 7816.70768107842 17737.2824008391 69 11908.8939136802 6620.370238292 17197.4175890683 70 11299.1377226850 5602.17672937129 16996.0987159986 71 12607.8120617308 5579.20203342722 19636.4220900345 72 11184.1087743144 4539.17215568877 17829.0453929401

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/19sds1259861082.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/19sds1259861082.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/263i61259861082.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/263i61259861082.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/3jk431259861082.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259861166kf3snmj64ndsz6w/3jk431259861082.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

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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