*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: Sun, 19 Dec 2010 13:39:31 +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/Dec/19/t1292765910f45ywl3b36yded9.htm/, Retrieved Sun, 19 Dec 2010 14:38:34 +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/2010/Dec/19/t1292765910f45ywl3b36yded9.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:

Dataseries X:

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19876 45335 48674 156392 100837 101605 532850 294189 80763 105995 25045 90474 48481 50730 68694 207716 99132 104012 422632 364974 82687 66834 28408 97073 40284 24421 116346 72120 108751 91738 402216 390070 106045 110070 70668 167841 28607 95371 30605 131063 81214 85451 455196 454570 63114 74287 42350 113375

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 0 beta 0 gamma 0.689793581003217 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 48481 44449.8456196582 4031.15438034176 14 50730 48323.6072746699 2406.39272533011 15 68694 63239.7855963482 5454.21440365177 16 207716 203795.04725136 3920.95274864012 17 99132 96684.3505730382 2447.64942696178 18 104012 101130.98722805 2881.01277195013 19 422632 531762.040549728 -109130.040549728 20 364974 291666.093871407 73307.9061285935 21 82687 77162.8555264182 5524.14447358181 22 66834 99403.9088480965 -32569.9088480965 23 28408 16368.1705031082 12039.8294968918 24 97073 81749.6404914532 15323.3595085468 25 40284 47011.1498953909 -6727.14989539092 26 24421 49764.1613901154 -25343.1613901154 27 116346 66782.7075415424 49563.2924584576 28 72120 206280.335148929 -134160.335148929 29 108751 98153.3632964426 10597.6367035574 30 91738 102898.931205069 -11160.9312050693 31 402216 456265.478944045 -54049.4789440448 32 390070 342014.056815837 48055.9431841634 33 106045 80754.0147849692 25290.9852150308 34 110070 76718.0346509596 33351.9653490404 35 70668 24453.8074665773 46214.1925334227 36 167841 92100.2353799933 75740.7646200067 37 28607 42151.4449392437 -13544.4449392437 38 95371 32063.2512010251 63307.7487989749 39 30605 100751.788392912 -70146.7883929115 40 131063 113518.036998097 17544.9630019027 41 81214 105244.184928501 -24030.1849285005 42 85451 94980.832361934 -9529.83236193392 43 455196 418763.135172014 36432.864827986 44 454570 374943.377813468 79626.6221865322 45 63114 97980.2139036847 -34866.2139036847 46 74287 99504.6461227093 -25217.6461227093 47 42350 56112.700687519 -13762.700687519 48 113375 144126.368495289 -30751.3684952894 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 49 32589.2136220418 -58624.6790742502 123803.106318334 50 75513.169810462 -15700.7228858299 166727.062506754 51 52145.6238916301 -39068.2688046619 143359.516587922 52 125401.079715889 34187.1870195966 216614.972412181 53 88448.9574746405 -2764.93522165153 179662.850170932 54 88187.855030775 -3026.03766551698 179401.747727067 55 443674.931328056 352461.038631764 534888.824024348 56 429649.950534846 338436.057838554 520863.843231138 57 73710.3632191777 -17503.5294771143 164924.255915470 58 81890.3155593935 -9323.57713689846 173104.208255686 59 46399.9179561396 -44813.9747401524 137613.810652432 60 122694.911760314 31481.019064022 213908.804456606

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/157n21292765968.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/157n21292765968.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/257n21292765968.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/257n21292765968.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/3fynn1292765968.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292765910f45ywl3b36yded9/3fynn1292765968.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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