ws9 techniek 4 forcasting

*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: Fri, 11 Dec 2009 03:43:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu.htm/, Retrieved Fri, 11 Dec 2009 11:52:24 +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/2009/Dec/11/t1260528739v1ocfbomc3f8yqu.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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100 96.21064363 96.31280765 107.1793443 114.9066592 92.56060184 114.9995356 107.1236185 117.7765394 107.3650971 106.2970187 114.5072908 98.0031578 103.0649206 100.2879168 104.6066685 111.1544534 104.9874617 109.9284852 111.5352466 132.4974459 100.3436426 123.0983561 114.2379493 104.569518 109.0833101 106.9843039 133.6769759 124.8537197 122.5132349 116.8013374 116.0118882 129.7575926 125.1973623 143.7912139 127.9465032 130.2962757 108.4424631 129.3675118 143.6797622 131.8844618 117.6186496 118.9560695 104.8202842 134.624315 140.401226 143.8005015 153.4317823 153.2924677 127.3149438 153.5525216 136.9276493 131.7730101 144.3391845 107.4208229 113.6249652 124.2221603 102.0618557 96.36853348 111.6838488

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.55295284543749 beta 0 gamma 0.87258335845831 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 98.0031578 96.6849941902412 1.31816360975880 14 103.0649206 102.729919771101 0.335000828898856 15 100.2879168 99.6531597024275 0.634757097572475 16 104.6066685 104.261594293772 0.345074206227878 17 111.1544534 110.849694786215 0.304758613785467 18 104.9874617 104.457056566090 0.530405133909838 19 109.9284852 118.600549445868 -8.67206424586843 20 111.5352466 106.080399369838 5.45484723016195 21 132.4974459 119.735807310015 12.7616385899850 22 100.3436426 115.790977365521 -15.4473347655211 23 123.0983561 106.713004957561 16.3853511424389 24 114.2379493 124.582167311732 -10.3442180117317 25 104.569518 102.222365040111 2.34715295988909 26 109.0833101 108.719398124416 0.363911975583534 27 106.9843039 105.581063343598 1.40324055640188 28 133.6769759 110.737731176471 22.9392447235295 29 124.8537197 130.903104883016 -6.04938518301611 30 122.5132349 120.089655804670 2.42357909532954 31 116.8013374 133.091280991619 -16.2899435916185 32 116.0118882 121.495298450408 -5.4834102504085 33 129.7575926 132.515410863898 -2.75781826389837 34 125.1973623 108.639837588287 16.5575247117133 35 143.7912139 130.993220380299 12.7979935197014 36 127.9465032 135.985594812993 -8.03909161299299 37 130.2962757 118.100347984874 12.1959277151264 38 108.4424631 130.083515431763 -21.6410523317633 39 129.3675118 114.914096618064 14.4534151819358 40 143.6797622 136.501962569653 7.17779963034687 41 131.8844618 136.327549068236 -4.44308726823581 42 117.6186496 129.389904257857 -11.7712546578571 43 118.9560695 126.796296925452 -7.8402274254519 44 104.8202842 124.085632563013 -19.2653483630133 45 134.624315 128.167866338530 6.45644866147046 46 140.401226 116.201225937770 24.2000000622302 47 143.8005015 141.537651688209 2.26284981179072 48 153.4317823 132.490592719048 20.9411895809517 49 153.2924677 137.526868906653 15.7655987933468 50 127.3149438 136.266407416698 -8.95146361669761 51 153.5525216 143.849087598108 9.70343400189162 52 136.9276493 161.564637853673 -24.6369885536727 53 131.7730101 138.940612081119 -7.16760198111947 54 144.3391845 127.226253257054 17.1129312429455 55 107.4208229 142.819436773032 -35.3986138730316 56 113.6249652 119.585715351972 -5.96075015197157 57 124.2221603 143.378525102862 -19.1563648028615 58 102.0618557 123.304085676272 -21.2422299762719 59 96.36853348 114.336595284823 -17.9680618048235 60 111.6838488 101.81360122127 9.87024757872994 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 101.059596891796 75.9540972253128 126.165096558279 62 88.0403960322358 59.8646351150197 116.216156949452 63 101.674522717695 67.9879186353936 135.361126799996 64 100.48070462375 63.9988507218644 136.962558525636 65 98.904363087092 59.9893066988752 137.819419475309 66 99.9121345935185 58.1063903635552 141.717878823482 67 88.4510747159663 47.5804235382225 129.32172589371 68 94.768502365894 49.3206767130205 140.216328018767 69 112.567952337536 58.2646839814761 166.871220693595 70 102.562998970744 50.3714650725433 154.754532868944 71 105.930266470035 50.4139746882573 161.446558251813 72 114.688153885615 -2.35476202226654 231.731069793497

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/13i0p1260528197.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/13i0p1260528197.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/2d0mm1260528197.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/2d0mm1260528197.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/3joub1260528197.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528739v1ocfbomc3f8yqu/3joub1260528197.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')

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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