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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 14:16:37 -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/t1212005911bbc02srrbhmkwjk.htm/, Retrieved Wed, 28 May 2008 22:18:31 +0200

User-defined keywords:

Dataseries X:

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101,6 101,8 102,1 102,1 101,9 102,1 102 102,1 102,2 102,3 102,7 102,8 103,1 103,1 103,3 103,5 103,3 103,5 103,8 103,9 103,9 104,2 104,6 104,9 105,2 105,2 105,6 105,6 106,2 106,3 106,4 106,9 107,2 107,3 107,3 107,4 107,55 107,87 108,37 108,38 107,92 108,03 108,14 108,3 108,64 108,66 109,04 109,03 109,03 109,54 109,75 109,83 109,65 109,82 109,95 110,12 110,15 110,2 109,99 110,14 110,14 110,81 110,97 110,99 109,73 109,81 110,02 110,18 110,21 110,25 110,36 110,51 110,64 110,95 111,18 111,19 111,69 111,7 111,83 111,77 111,73 112,01 111,86 112,04

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.963580582065361 beta 0.0293940647936531 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 103.1 101.902722222222 1.19727777777773 14 103.1 103.267319678465 -0.167319678465049 15 103.3 103.312278436247 -0.0122784362469446 16 103.5 103.506284155546 -0.00628415554575668 17 103.3 103.705887857737 -0.405887857737483 18 103.5 103.508945006917 -0.00894500691718747 19 103.8 103.694235224986 0.105764775014251 20 103.9 103.993053195396 -0.0930531953964362 21 103.9 104.097658433315 -0.197658433315397 22 104.2 104.095869706662 0.104130293338088 23 104.6 104.387828076474 0.212171923525588 24 104.9 104.789902725288 0.110097274711791 25 105.2 105.096738570256 0.103261429743966 26 105.2 105.399912258026 -0.199912258025790 27 105.6 105.405291442419 0.194708557580952 28 105.6 105.796434419588 -0.196434419588115 29 106.2 105.805115899029 0.394884100971495 30 106.3 106.394764942299 -0.0947649422987666 31 106.4 106.509913595859 -0.109913595859467 32 106.9 106.607352157770 0.292647842230295 33 107.2 107.100979930322 0.0990200696781613 34 107.3 107.410836340995 -0.110836340994950 35 107.3 107.515339910669 -0.215339910668519 36 107.4 107.513046679108 -0.113046679107711 37 107.55 107.606119335880 -0.056119335880453 38 107.87 107.752456576356 0.117543423643795 39 108.37 108.069461126782 0.3005388732184 40 108.38 108.571308866845 -0.191308866844935 41 107.92 108.593803128983 -0.673803128982883 42 108.03 108.132290792510 -0.102290792510303 43 108.14 108.218579407491 -0.0785794074908495 44 108.3 108.325490204868 -0.0254902048680208 45 108.64 108.482834753916 0.157165246083821 46 108.66 108.820634026426 -0.160634026425569 47 109.04 108.847658365061 0.192341634938913 48 109.03 109.220250994856 -0.190250994855532 49 109.03 109.218796212161 -0.188796212161364 50 109.54 109.213395850856 0.326604149144458 51 109.75 109.713875858663 0.0361241413373961 52 109.83 109.935478135394 -0.105478135394250 53 109.65 110.017647692643 -0.367647692642620 54 109.82 109.836782667490 -0.0167826674896503 55 109.95 109.993529022777 -0.0435290227770935 56 110.12 110.123270213013 -0.00327021301272623 57 110.15 110.291711386552 -0.141711386552387 58 110.2 110.322739563959 -0.122739563959357 59 109.99 110.368572201039 -0.378572201038821 60 110.14 110.157166968081 -0.0171669680812983 61 110.14 110.293518570379 -0.15351857037858 62 110.81 110.294136225455 0.515863774545039 63 110.97 110.954368803521 0.0156311964787932 64 110.99 111.133029713822 -0.143029713822330 65 109.73 111.154756942565 -1.4247569425645 66 109.81 109.901082527596 -0.0910825275957592 67 110.02 109.929931101158 0.0900688988419489 68 110.18 110.135884742615 0.0441152573853856 69 110.21 110.298807848190 -0.0888078481895747 70 110.25 110.331133476790 -0.0811334767904697 71 110.36 110.368555992559 -0.00855599255943673 72 110.51 110.475670426745 0.0343295732550217 73 110.64 110.625080894787 0.0149191052130391 74 110.95 110.756210374758 0.193789625241720 75 111.18 111.065184824685 0.114815175314590 76 111.19 111.301313001550 -0.111313001549519 77 111.69 111.316395678757 0.373604321242553 78 111.7 111.809317072811 -0.10931707281145 79 111.83 111.833808541307 -0.0038085413065545 80 111.77 111.959858110592 -0.189858110591643 81 111.73 111.901256471912 -0.171256471911761 82 112.01 111.855728419803 0.154271580197417 83 111.86 112.128242396448 -0.268242396448429 84 112.04 111.986032532602 0.0539674673977686 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 112.155826387173 NA NA 86 112.273618238096 NA NA 87 112.391410089018 NA NA 88 112.509201939941 NA NA 89 112.626993790864 NA NA 90 112.744785641787 NA NA 91 112.862577492710 NA NA 92 112.980369343633 NA NA 93 113.098161194555 NA NA 94 113.215953045478 NA NA 95 113.333744896401 NA NA 96 113.451536747324 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/1jj851212005791.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/1jj851212005791.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/2jv981212005791.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/2jv981212005791.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/34hei1212005791.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212005911bbc02srrbhmkwjk/34hei1212005791.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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