ES-Model - Uitvoer

*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: Tue, 07 Dec 2010 08:23:30 +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/07/t1291710106m0ykuor1tp9b3k5.htm/, Retrieved Tue, 07 Dec 2010 09:21:46 +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/07/t1291710106m0ykuor1tp9b3k5.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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16198,9 16554,2 19554,2 15903,8 18003,8 18329,6 16260,7 14851,9 18174,1 18406,6 18466,5 16016,5 17428,5 17167,2 19630 17183,6 18344,7 19301,4 18147,5 16192,9 18374,4 20515,2 18957,2 16471,5 18746,8 19009,5 19211,2 20547,7 19325,8 20605,5 20056,9 16141,4 20359,8 19711,6 15638,6 14384,5 13855,6 14308,3 15290,6 14423,8 13779,7 15686,3 14733,8 12522,5 16189,4 16059,1 16007,1 15806,8 15160 15692,1 18908,9 16969,9 16997,5 19858,9 17681,2

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 0.622309773779561 beta 0 gamma 0.742362409692478 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 17428.5 16963.6914457071 464.808554292926 14 17167.2 16857.1546853132 310.045314686755 15 19630 19448.6780816240 181.321918375961 16 17183.6 17018.9123169632 164.687683036809 17 18344.7 18174.1949050714 170.505094928558 18 19301.4 19197.5977254580 103.802274541973 19 18147.5 17067.4115621127 1080.08843788728 20 16192.9 16253.9861535563 -61.086153556269 21 18374.4 19509.4716431556 -1135.0716431556 22 20515.2 18979.1221323465 1536.07786765349 23 18957.2 19927.4092360071 -970.209236007075 24 16471.5 16818.9427124953 -347.44271249534 25 18746.8 18025.9418125222 720.858187477828 26 19009.5 18035.3542559273 974.145744072674 27 19211.2 21004.0619847831 -1792.86198478308 28 20547.7 17341.0783247009 3206.62167529907 29 19325.8 20391.0172709386 -1065.21727093861 30 20605.5 20626.7156467150 -21.2156467150235 31 20056.9 18692.4636782381 1364.4363217619 32 16141.4 17736.0247513087 -1594.62475130867 33 20359.8 19736.0468811166 623.753118883385 34 19711.6 21049.1761940425 -1337.57619404248 35 15638.6 19506.4399253606 -3867.83992536057 36 14384.5 14769.3626656972 -384.862665697196 37 13855.6 16252.6084026105 -2397.00840261047 38 14308.3 14392.7595253442 -84.4595253442058 39 15290.6 15926.8648472283 -636.264847228269 40 14423.8 14385.4132494946 38.3867505053895 41 13779.7 14265.9775041320 -486.277504131951 42 15686.3 15154.6760902448 531.623909755175 43 14733.8 13952.9748736252 780.825126374813 44 12522.5 11803.6784965886 718.821503411446 45 16189.4 15865.3763428862 324.023657113756 46 16059.1 16442.0576336315 -382.957633631491 47 16007.1 14783.9468226102 1223.15317738981 48 15806.8 14191.6120341686 1615.18796583136 49 15160 16355.3373157533 -1195.33731575325 50 15692.1 15891.6995537380 -199.599553737955 51 18908.9 17199.4352644359 1709.46473556411 52 16969.9 17306.9149694926 -337.014969492571 53 16997.5 16806.7561130939 190.743886906082 54 19858.9 18402.1740069654 1456.72599303462 55 17681.2 17846.0446498263 -164.844649826282 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 56 15090.8639648342 12692.1140424690 17489.6138871993 57 18594.5375489734 15769.2322393922 21419.8428585546 58 18771.3501970153 15575.9317588997 21966.7686351308 59 17801.8838743615 14274.9804312616 21328.7873174613 60 16558.2888092593 12728.4850545937 20388.0925639249 61 16928.8432488389 12818.3997567627 21039.2867409151 62 17488.2635486490 13115.1531448457 21861.3739524523 63 19455.4812356104 14834.6108082825 24076.3516629383 64 17925.3461545130 13069.3403463972 22781.3519626288 65 17782.8896329347 12702.6198260489 22863.1594398205 66 19614.5656360491 14319.5217067643 24909.6095653339 67 17697.2405712710 12195.8008401318 23198.6803024102

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/1qny21291710206.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/1qny21291710206.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/21wx51291710206.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/21wx51291710206.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/31wx51291710206.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/07/t1291710106m0ykuor1tp9b3k5/31wx51291710206.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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