Exponential Smoothing - king size sigarets - Vincent Bruyninckx

*Unverified author*

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 05:41:56 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0.htm/, Retrieved Sat, 06 Jun 2009 13:42:33 +0200

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/Jun/06/t1244288549w3rv1ixd8digtc0.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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2.98 2.98 2.98 3.03 3.07 3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.08 3.12 3.15 3.15 3.15 3.15 3.16 3.19 3.2 3.2 3.2 3.21 3.21 3.21 3.21 3.21 3.28 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.45 3.49 3.5 3.54 3.64 3.67 3.67 3.68 3.68 3.68 3.68 3.7 3.83 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.88 3.88 3.88 3.88 3.88 3.88 3.89 3.89 3.91 3.95 3.99 3.99 3.99

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 0.865625929532432 beta 0.0279541213592297 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.08 3.03218057162422 0.0478194283757842 14 3.08 3.07658651044536 0.00341348955464138 15 3.12 3.12098274303256 -0.000982743032556854 16 3.15 3.14988596042865 0.000114039571347480 17 3.15 3.14932298003238 0.000677019967616932 18 3.15 3.14926600305820 0.000733996941795212 19 3.15 3.18347764010211 -0.0334776401021055 20 3.16 3.15453549263141 0.00546450736859105 21 3.19 3.15770769408078 0.0322923059192242 22 3.2 3.18394027046506 0.0160597295349381 23 3.2 3.19905688057097 0.000943119429031913 24 3.2 3.20325491989269 -0.00325491989269056 25 3.21 3.21086127093729 -0.000861270937285497 26 3.21 3.20715838246823 0.00284161753176626 27 3.21 3.25229595455108 -0.0422959545510846 28 3.21 3.2457125917697 -0.0357125917696992 29 3.21 3.2126444686849 -0.00264446868490165 30 3.28 3.20808922545219 0.0719107745478067 31 3.3 3.3003046227353 -0.000304622735299631 32 3.3 3.30623521015310 -0.00623521015310402 33 3.3 3.30334739022062 -0.00334739022061781 34 3.3 3.29601239739219 0.00398760260781206 35 3.3 3.29796278441105 0.00203721558895253 36 3.3 3.30199796556584 -0.00199796556583953 37 3.3 3.31074846677059 -0.0107484667705950 38 3.45 3.29810415408185 0.151895845918155 39 3.49 3.47106178845088 0.0189382115491159 40 3.5 3.52483229925198 -0.0248322992519761 41 3.54 3.50996579023465 0.0300342097653479 42 3.64 3.54914710678076 0.0908528932192354 43 3.67 3.65529901461614 0.0147009853838607 44 3.67 3.67942078021977 -0.00942078021977322 45 3.68 3.67980709253619 0.000192907463814951 46 3.68 3.68149108074878 -0.00149108074877935 47 3.68 3.68343826048178 -0.00343826048177487 48 3.68 3.68744456719865 -0.00744456719865161 49 3.7 3.69629999235367 0.00370000764632605 50 3.83 3.72464933952557 0.105350660474434 51 3.87 3.84581775496138 0.0241822450386211 52 3.87 3.90557337660747 -0.0355733766074660 53 3.87 3.89401496738218 -0.0240149673821812 54 3.87 3.89886491323324 -0.0288649132332428 55 3.87 3.89217940142879 -0.0221794014287879 56 3.87 3.88073831118437 -0.0107383111843657 57 3.87 3.8809594803103 -0.0109594803102966 58 3.87 3.87175396268486 -0.00175396268486416 59 3.87 3.87229346628109 -0.00229346628108607 60 3.88 3.87604616335871 0.00395383664128701 61 3.88 3.89638452904704 -0.0163845290470395 62 3.88 3.92135090838234 -0.041350908382344 63 3.88 3.90061684364766 -0.0206168436476633 64 3.88 3.90846348793655 -0.0284634879365453 65 3.88 3.89967136198188 -0.0196713619818771 66 3.89 3.90279039115096 -0.0127903911509573 67 3.89 3.90646336068969 -0.0164633606896918 68 3.91 3.89715692277955 0.0128430772204462 69 3.95 3.91396290779253 0.0360370922074695 70 3.99 3.94381782751663 0.0461821724833702 71 3.99 3.98396229241338 0.00603770758662137 72 3.99 3.99427826004811 -0.00427826004810994 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4.00329788648877 3.93648291852419 4.07011285445336 74 4.03867118399632 3.94902471892985 4.1283176490628 75 4.05662932358499 3.9480854794548 4.16517316771517 76 4.08221441507228 3.95660646550514 4.20782236463943 77 4.10060152418589 3.95935695784649 4.24184609052528 78 4.12379265877942 3.96761954582187 4.27996577173698 79 4.1401058024406 3.96984629302767 4.31036531185352 80 4.15113930065952 3.96745713829760 4.33482146302144 81 4.16173200979754 3.96501009480972 4.35845392478536 82 4.16215333036473 3.95313680895044 4.37116985177901 83 4.15613418551383 3.9353865146638 4.37688185636385 84 4.15929595911847 -0.521679996993567 8.8402719152305

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/1kgid1244288514.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/1kgid1244288514.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/23ij61244288514.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/23ij61244288514.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/3cj7y1244288514.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244288549w3rv1ixd8digtc0/3cj7y1244288514.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')

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Software written by Ed van Stee & Patrick Wessa

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