exponential smoothing - hondenvoeding - Peter De Klerck

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 30 May 2008 05:13:16 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy.htm/, Retrieved Fri, 30 May 2008 11:15:22 +0000

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2,02 1,99 1,99 2,01 2,01 2,01 2 2,01 2,02 2,01 2 2,01 2,01 2,01 2 2 1,98 2,01 1,99 1,99 2 2 1,99 1,96 1,98 1,98 1,99 1,99 1,99 1,99 1,98 1,98 1,98 1,98 1,98 1,98 1,97 1,99 2 1,99 1,98 1,98 1,96 1,95 1,94 1,93 1,92 1,91 1,92 1,93 1,94 1,93 1,94 1,93 1,93 1,92 1,92 1,91 1,92 1,92 1,93 1,91 1,95 2,01 1,98 2,01 2 1,99 1,98 1,98 1,99 1,98 1,99

Text written by user:

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 0.605336936283191 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2.01 2.01751358695652 -0.00751358695652193 14 2.01 2.01421533524776 -0.00421533524776363 15 2 2.00333030379014 -0.00333030379014243 16 2 2.00256434789693 -0.00256434789692506 17 1.98 1.98184538673077 -0.00184538673076973 18 2.01 2.01322830598091 -0.00322830598090773 19 1.99 1.99460742646237 -0.00460742646237389 20 1.99 1.99431838104349 -0.00431838104349036 21 2 2.00337097215959 -0.00337097215958737 22 2 2.00216373153354 -0.00216373153353988 23 1.99 1.99085394491609 -0.000853944916087368 24 1.96 1.96075368718350 -0.000753687183495222 25 1.98 1.99108211724516 -0.0110821172451585 26 1.98 1.98692540046873 -0.00692540046873091 27 1.99 1.97474915565967 0.0152508443403274 28 1.99 1.98553334954787 0.00446665045213268 29 1.99 1.96935425879787 0.0206457412021290 30 1.99 2.01380610137633 -0.0238061013763311 31 1.98 1.98218443432322 -0.00218443432321935 32 1.98 1.98347619109306 -0.00347619109305985 33 1.98 1.99341249818623 -0.0134124981862327 34 1.98 1.98660320424373 -0.00660320424372718 35 1.98 1.97312296521644 0.00687703478356383 36 1.98 1.94774212307360 0.0322578769263955 37 1.97 1.99397742236394 -0.0239774223639444 38 1.99 1.98365520367246 0.00634479632753804 39 2 1.98826404385401 0.0117359561459911 40 1.99 1.99266442309164 -0.00266442309163506 41 1.98 1.97855391965379 0.00144608034621019 42 1.98 1.99383999797218 -0.0138399979721793 43 1.96 1.97678445478226 -0.0167844547822642 44 1.95 1.96872847121339 -0.0187284712133924 45 1.94 1.96551051638777 -0.0255105163877676 46 1.93 1.95406522198114 -0.0240652219811441 47 1.92 1.93533473106951 -0.015334731069508 48 1.91 1.90652516755554 0.00347483244445912 49 1.92 1.91314303137533 0.00685696862467466 50 1.93 1.93345306818452 -0.00345306818452329 51 1.94 1.93425859073116 0.00574140926884104 52 1.93 1.92934695153916 0.000653048460840244 53 1.94 1.91886690004729 0.0211330999527051 54 1.93 1.94003740799748 -0.0100374079974763 55 1.93 1.92412164462714 0.00587835537286097 56 1.92 1.92901706564451 -0.00901706564451343 57 1.92 1.92900116058617 -0.00900116058617262 58 1.91 1.92811999335899 -0.0181199933589866 59 1.92 1.91643397121793 0.00356602878207157 60 1.92 1.90648917572954 0.0135108242704611 61 1.93 1.92051700032063 0.00948299967937016 62 1.91 1.93834768000891 -0.0283476800089104 63 1.95 1.92771229514483 0.0222877048551680 64 2.01 1.93080855176411 0.079191448235886 65 1.98 1.97595341443952 0.00404658556048298 66 2.01 1.97447897595052 0.0355210240494754 67 2 1.99242277819048 0.00757722180951625 68 1.99 1.99246791331771 -0.00246791331770857 69 1.98 1.99642272920318 -0.0164227292031811 70 1.98 1.98745014588732 -0.00745014588731974 71 1.99 1.99078164846339 -0.000781648463390017 72 1.98 1.98212988680677 -0.0021298868067694 73 1.99 1.98510017767985 0.00489982232015462 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.98522611887879 1.95255472870596 2.01789750905162 75 2.01173454790498 1.97354348422169 2.04992561158826 76 2.02379703925004 1.98078895914064 2.06680511935944 77 1.99134749154445 1.9440100585328 2.03868492455610 78 1.99984530367270 1.94854257300884 2.05114803433655 79 1.98525853143699 1.93027573610059 2.04024132677338 80 1.97675245052374 1.91832090602559 2.03518399502189 81 1.97669373510500 1.91500594861630 2.03838152159370 82 1.98120358359130 1.91642302623563 2.04598414094697 83 1.99167674427737 1.92394449035986 2.05940899819489 84 1.98296604343161 1.91240546073715 2.05352662612608 85 1.99 1.91672017030848 2.06327982969152

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/1b5gl1212145989.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/1b5gl1212145989.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/2cyd81212145989.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/2cyd81212145989.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/37fxf1212145989.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212146122v4bbevm7ibvtvpy/37fxf1212145989.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=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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