Exponential smoothing - gemiddelde prijs strip - Dellaert Kenny

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 04:12:59 -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/04/t1244110510v241o8y96pipoak.htm/, Retrieved Thu, 04 Jun 2009 12:15:10 +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/04/t1244110510v241o8y96pipoak.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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5,11 5,11 5,11 5,1 5,1 5,1 5,1 5,1 5,12 5,25 5,26 5,26 5,26 5,26 5,26 5,26 5,29 5,3 5,33 5,33 5,35 5,38 5,38 5,38 5,38 5,38 5,39 5,39 5,4 5,4 5,4 5,4 5,4 5,41 5,41 5,41 5,41 5,41 5,42 5,42 5,42 5,42 5,43 5,43 5,45 5,51 5,51 5,51 5,51 5,51 5,51 5,53 5,53 5,53 5,53 5,52 5,53 5,54 5,54 5,57 5,56 5,57 5,58 5,61 5,66 5,68 5,69 5,7 5,72 5,71 5,69 5,7 5,7

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0406582087810778 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 5.11 5.11 0 4 5.1 5.11 -0.0100000000000007 5 5.1 5.09959341791219 0.000406582087810747 6 5.1 5.0996099488116 0.000390051188397855 7 5.1 5.09962580759426 0.000374192405744544 8 5.1 5.09964102158721 0.000358978412787536 9 5.12 5.09965561700647 0.0203443829935335 10 5.25 5.12048278317774 0.129517216822260 11 5.26 5.25574872122004 0.00425127877995557 12 5.26 5.26592157060027 -0.00592157060026643 13 5.26 5.26568081014649 -0.00568081014648847 14 5.26 5.26544983858151 -0.00544983858150694 15 5.26 5.26522825790664 -0.00522825790663717 16 5.26 5.26501568630511 -0.00501568630510718 17 5.29 5.26481175748413 0.0251882425158660 18 5.3 5.29583586630717 0.00416413369282687 19 5.33 5.30600517252425 0.023994827475752 20 5.33 5.33698075922942 -0.00698075922942287 21 5.35 5.33669693406322 0.0133030659367765 22 5.38 5.35723781289551 0.0227621871044921 23 5.38 5.38816328265112 -0.00816328265111732 24 5.38 5.38783137820075 -0.0078313782007493 25 5.38 5.38751296839082 -0.00751296839081927 26 5.38 5.38720750455342 -0.00720750455341967 27 5.39 5.3869144603285 0.00308553967150349 28 5.39 5.39703991284466 -0.00703991284466277 29 5.4 5.39675368259842 0.00324631740157688 30 5.4 5.40688567204911 -0.00688567204910662 31 5.4 5.40660571295734 -0.00660571295733625 32 5.4 5.40633713650077 -0.00633713650076917 33 5.4 5.40607947988185 -0.00607947988184598 34 5.41 5.40583229911953 0.00416770088046992 35 5.41 5.41600175037207 -0.0060017503720653 36 5.41 5.41575772995239 -0.00575772995238566 37 5.41 5.41552363096588 -0.00552363096587616 38 5.41 5.41529905002484 -0.00529905002483666 39 5.42 5.41508360014259 0.00491639985741443 40 5.42 5.42528349215444 -0.00528349215443935 41 5.42 5.42506867482733 -0.00506867482733053 42 5.42 5.42486259158796 -0.00486259158795743 43 5.43 5.42466488732396 0.00533511267604236 44 5.43 5.43488180344901 -0.00488180344901057 45 5.45 5.43468331806515 0.0153166819348476 46 5.51 5.45530606691709 0.0546939330829064 47 5.51 5.51752982426744 -0.00752982426743642 48 5.51 5.51722367510029 -0.00722367510028565 49 5.51 5.51692997340989 -0.00692997340989177 50 5.51 5.51664821310414 -0.0066482131041452 51 5.51 5.51637790866774 -0.00637790866773535 52 5.53 5.51611859432554 0.0138814056744643 53 5.53 5.53668298741562 -0.00668298741562356 54 5.53 5.536411269118 -0.00641126911799805 55 5.53 5.53615059839965 -0.00615059839964616 56 5.52 5.53590052608579 -0.0159005260857858 57 5.53 5.52525403917646 0.00474596082354051 58 5.54 5.53544700144249 0.00455299855750901 59 5.54 5.54563211820842 -0.00563211820842202 60 5.57 5.54540312637042 0.0245968736295765 61 5.56 5.57640319119382 -0.0164031911938176 62 5.57 5.56573626682158 0.00426373317841744 63 5.58 5.57590962257534 0.00409037742466190 64 5.61 5.58607592999466 0.0239240700053376 65 5.66 5.61704863982783 0.0429513601721663 66 5.68 5.66879496519714 0.0112050348028552 67 5.69 5.68925054184156 0.000749458158442629 68 5.7 5.69928101346784 0.000718986532162624 69 5.72 5.70931024617237 0.0106897538276272 70 5.71 5.72974487241531 -0.0197448724153144 71 5.69 5.7189420812703 -0.0289420812702961 72 5.7 5.69776534808745 0.00223465191254935 73 5.7 5.70785620503146 -0.00785620503146323 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 5.70753678580707 5.66785720325831 5.74721636835583 75 5.71507357161413 5.65780602860326 5.77234111462501 76 5.7226103574212 5.65105260373647 5.79416811110594 77 5.73014714322827 5.64587083196832 5.81442345448822 78 5.73768392903534 5.64160723809176 5.83376061997891 79 5.7452207148424 5.63793409265545 5.85250733702936 80 5.75275750064947 5.63466106382316 5.87085393747579 81 5.76029428645654 5.63166698261458 5.8889215902985 82 5.76783107226361 5.62886967659322 5.90679246793399 83 5.77536785807067 5.62621078499425 5.9245249311471 84 5.78290464387774 5.62364737510021 5.94216191265527 85 5.79044142968481 5.62114698029397 5.95973587907565

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/16ft01244110374.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/16ft01244110374.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/2fgwk1244110374.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/2fgwk1244110374.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/3dpqd1244110374.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244110510v241o8y96pipoak/3dpqd1244110374.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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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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