*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 05:26:58 -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/t1259929653d904n9lhrv9o3hx.htm/, Retrieved Fri, 04 Dec 2009 13:27:37 +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/t1259929653d904n9lhrv9o3hx.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 «

20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036

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 0.272554654406546 beta 0.00487076338884115 gamma 0.70455888173589 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 19684 19339.8654646862 344.134535313824 14 19785 19398.2650313627 386.734968637258 15 18479 18127.0426576304 351.957342369627 16 10698 10574.3386406903 123.661359309668 17 31956 31996.5879679259 -40.5879679259233 18 29506 29717.4998941825 -211.499894182511 19 34506 29962.6849511905 4543.31504880952 20 27165 28706.3430014938 -1541.34300149381 21 26736 24192.2071758607 2543.79282413933 22 23691 30373.4273873151 -6682.42738731514 23 18157 19079.1179697570 -922.117969757048 24 17328 19477.4696161048 -2149.46961610479 25 18205 19770.2684824669 -1565.26848246688 26 20995 19324.2509767584 1670.74902324159 27 17382 18374.3927816361 -992.39278163606 28 9367 10461.7862917639 -1094.78629176393 29 31124 30444.8745887772 679.125411222823 30 26551 28364.7051988498 -1813.70519884984 31 30651 30358.3210085617 292.678991438297 32 25859 25323.6848347909 535.315165209082 33 25100 23576.0548430538 1523.94515694622 34 25778 24479.4150415233 1298.58495847671 35 20418 18378.5365959101 2039.46340408991 36 18688 18917.0586264496 -229.058626449591 37 20424 20081.4043989695 342.595601030476 38 24776 21934.1863125973 2841.81368740273 39 19814 19649.8670652997 164.132934700316 40 12738 11062.5342039917 1675.46579600831 41 31566 36937.217983932 -5371.21798393202 42 30111 31395.3813805006 -1284.38138050062 43 30019 35153.946987579 -5134.94698757902 44 31934 28243.0072775851 3690.99272241495 45 25826 27656.0316092446 -1830.03160924464 46 26835 27552.0915144511 -717.091514451073 47 20205 20803.1605363178 -598.160536317813 48 17789 19417.1863121286 -1628.18631212860 49 20520 20507.2835686475 12.7164313524845 50 22518 23520.0257811739 -1002.02578117390 51 15572 18978.8641190882 -3406.8641190882 52 11509 10844.768605237 664.231394763003 53 25447 30338.2051874438 -4891.20518744384 54 24090 27230.2409035813 -3140.24090358134 55 27786 28121.3150033911 -335.315003391053 56 26195 27071.8651917856 -876.86519178559 57 20516 22997.6051509559 -2481.60515095589 58 22759 23130.5468843130 -371.546884313033 59 19028 17479.637946904 1548.36205309599 60 16971 16336.7594453119 634.240554688129 61 20036 18664.9886128268 1371.01138717317 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 21336.5418553715 17910.9758511718 24762.1078595713 63 16085.1277203214 12543.8051440110 19626.4502966318 64 11027.1445939128 7451.99614218337 14602.2930456422 65 26883.0961539378 21743.7515991900 32022.4407086856 66 25935.8141318640 20762.5404747996 31109.0877889283 67 29267.20648433 23545.1851406956 34989.2278279644 68 27962.0320428745 22281.5454713333 33642.5186144158 69 22982.7663777064 17824.2638716797 28141.268883733 70 25045.3910148591 19464.8196005822 30625.9624291359 71 20017.5651818446 15009.6361438475 25025.4942198416 72 17835.4580831857 12988.8679906526 22682.0481757187 73 20502.6317188131 16323.9943350587 24681.2691025675

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/1puvk1259929615.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/1puvk1259929615.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/23xlw1259929615.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/23xlw1259929615.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/3exaa1259929615.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929653d904n9lhrv9o3hx/3exaa1259929615.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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