exponential smoothing vruchtensappen - sanne peelmans

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 09:43:03 -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/28/t1211989437k9mxsvmiklz9umw.htm/, Retrieved Wed, 28 May 2008 17:43:57 +0200

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Dataseries X:

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1,08 1,08 1,09 1,1 1,1 1,11 1,1 1,1 1,11 1,11 1,11 1,11 1,11 1,12 1,11 1,11 1,12 1,12 1,11 1,12 1,11 1,11 1,1 1,1 1,1 1,11 1,1 1,1 1,09 1,1 1,1 1,11 1,13 1,13 1,13 1,13 1,14 1,14 1,14 1,15 1,15 1,15 1,15 1,15 1,15 1,14 1,14 1,14 1,13 1,12 1,13 1,13 1,13 1,12 1,13 1,12 1,12 1,11 1,11 1,11 1,11 1,14 1,15 1,15 1,16 1,15 1,16 1,13 1,13 1,12 1,12 1,11 1,11

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.726841894609817 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.11 1.10715126811594 0.00284873188405754 14 1.12 1.11797184579579 0.00202815420421376 15 1.11 1.10861265990680 0.00138734009319519 16 1.11 1.10962103680861 0.000378963191389081 17 1.12 1.12031314979929 -0.000313149799294088 18 1.12 1.12091887273921 -0.000918872739211984 19 1.11 1.11108433086987 -0.00108433086987114 20 1.12 1.12112952709936 -0.00112952709936343 21 1.11 1.11114187281578 -0.00114187281578260 22 1.11 1.11114524514829 -0.00114524514828895 23 1.1 1.10197949966158 -0.00197949966158073 24 1.1 1.10262404971051 -0.00262404971051144 25 1.1 1.10524493465159 -0.0052449346515866 26 1.11 1.10995854896797 4.14510320287942e-05 27 1.1 1.09898030041282 0.00101969958718162 28 1.1 1.09944601446868 0.000553985531318357 29 1.09 1.11007628475527 -0.0200762847552671 30 1.1 1.09615187510970 0.00384812489030328 31 1.1 1.0897369905995 0.0102630094004992 32 1.11 1.10801756341347 0.00198243658652775 33 1.13 1.10028844237879 0.0297115576212050 34 1.13 1.12271645936538 0.00728354063462477 35 1.13 1.11944922512412 0.0105507748758837 36 1.13 1.12902523958764 0.000974760412356446 37 1.14 1.13354597453182 0.00645402546818485 38 1.14 1.14820690228432 -0.00820690228431742 39 1.14 1.13150062149923 0.00849937850077342 40 1.15 1.13727566597856 0.0127243340214351 41 1.15 1.15111652987460 -0.00111652987459743 42 1.15 1.15750801079919 -0.00750801079919339 43 1.15 1.1445912888081 0.00540871119190034 44 1.15 1.15708164873372 -0.00708164873372219 45 1.15 1.15033880491794 -0.000338804917936919 46 1.14 1.14479856483514 -0.00479856483514229 47 1.14 1.13364202167857 0.00635797832142959 48 1.14 1.13755476998270 0.00244523001730146 49 1.13 1.14464100950208 -0.0146410095020753 50 1.12 1.13996443082180 -0.0199644308217972 51 1.13 1.11927574172597 0.0107242582740326 52 1.13 1.12782200288036 0.00217799711963784 53 1.13 1.13021660312270 -0.000216603122695336 54 1.12 1.13551630369265 -0.0155163036926533 55 1.13 1.12030712622923 0.009692873770774 56 1.12 1.13249955194757 -0.0124995519475688 57 1.12 1.12366061153668 -0.0036606115366804 58 1.11 1.11448772366811 -0.00448772366811201 59 1.11 1.10660461308566 0.00339538691433972 60 1.11 1.10729522692488 0.00270477307511996 61 1.11 1.10990286839678 9.71316032214453e-05 62 1.14 1.11448445243861 0.0255155475613873 63 1.15 1.13523538116796 0.0147646188320447 64 1.15 1.14438386514014 0.00561613485986179 65 1.16 1.14862334346614 0.0113766565338573 66 1.15 1.15817027362885 -0.00817027362884626 67 1.16 1.15518658972921 0.00481341027078841 68 1.13 1.15777037598931 -0.0277703759893106 69 1.13 1.14024638911596 -0.0102463891159645 70 1.12 1.12606074981142 -0.00606074981142313 71 1.12 1.11918763347798 0.000812366522019659 72 1.11 1.11781215311355 -0.00781215311355288 73 1.11 1.11206335362500 -0.00206335362500409 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.12201785283543 1.10315299952405 1.14088270614681 75 1.12128630931036 1.097964748263 1.14460787035771 76 1.11720426720843 1.09015047396402 1.14425806045283 77 1.11893523661904 1.08860504954186 1.14926542369621 78 1.11487373378291 1.08158810974847 1.14815935781735 79 1.12137514554215 1.08537590545868 1.15737438562563 80 1.11155981824025 1.07303764532888 1.15008199115161 81 1.11900732311821 1.07811758938175 1.15989705685467 82 1.11341252999390 1.07028501158321 1.15654004840458 83 1.11282206797192 1.06756728520269 1.15807685074114 84 1.10850026814195 1.06121382312105 1.15578671316286 85 1.11 1.06076565830702 1.15923434169298

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/1nsuz1211989377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/1nsuz1211989377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/2f7ki1211989377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/2f7ki1211989377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/3c6vl1211989377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989437k9mxsvmiklz9umw/3c6vl1211989377.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')

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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