*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, 04 Dec 2009 08:34:14 -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/04/t1259940896757ftczxhxqw1lo.htm/, Retrieved Fri, 04 Dec 2009 16:35:00 +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/04/t1259940896757ftczxhxqw1lo.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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8 8,1 7,7 7,5 7,6 7,8 7,8 7,8 7,5 7,5 7,1 7,5 7,5 7,6 7,7 7,7 7,9 8,1 8,2 8,2 8,2 7,9 7,3 6,9 6,6 6,7 6,9 7 7,1 7,2 7,1 6,9 7 6,8 6,4 6,7 6,6 6,4 6,3 6,2 6,5 6,8 6,8 6,4 6,1 5,8 6,1 7,2 7,3 6,9 6,1 5,8 6,2 7,1 7,7 7,9 7,7 7,4 7,5 8 8,1

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.92852853543084 beta 1 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7.5 7.43325688014239 0.0667431198576134 14 7.6 7.64604691568444 -0.0460469156844354 15 7.7 7.69903709297351 0.000962907026494264 16 7.7 7.69656809567221 0.00343190432778773 17 7.9 7.92064617861872 -0.0206461786187218 18 8.1 8.14660566968208 -0.04660566968208 19 8.2 7.94548071586716 0.254519284132838 20 8.2 8.44899290291657 -0.248992902916571 21 8.2 7.9148830408396 0.285116959160407 22 7.9 8.42651571563598 -0.526515715635977 23 7.3 7.27373174719167 0.0262682528083253 24 6.9 7.47809936117529 -0.578099361175288 25 6.6 6.17893599945708 0.421064000542922 26 6.7 6.26944570361116 0.430554296388845 27 6.9 6.7679443784595 0.132055621540500 28 7 7.01977935011743 -0.0197793501174273 29 7.1 7.31337398152559 -0.213373981525590 30 7.2 7.26470807925219 -0.0647080792521857 31 7.1 6.99333165308493 0.106668346915072 32 6.9 7.0959413772399 -0.1959413772399 33 7 6.51725468240361 0.482745317596389 34 6.8 7.1734434987627 -0.373443498762699 35 6.4 6.40044617609966 -0.000446176099661244 36 6.7 6.61580361637285 0.0841963836271464 37 6.6 6.74078965616378 -0.140789656163782 38 6.4 6.52783593537739 -0.127835935377389 39 6.3 6.18277278400692 0.117227215993077 40 6.2 6.10059954029592 0.0994004597040838 41 6.5 6.26665897019514 0.233341029804856 42 6.8 6.83851412014025 -0.0385141201402517 43 6.8 6.84293848398286 -0.042938483982863 44 6.4 6.88007070462229 -0.480070704622288 45 6.1 5.93007759419789 0.169922405802114 46 5.8 5.79872786002459 0.00127213997541276 47 6.1 5.34920741810944 0.75079258189056 48 7.2 6.87864983507475 0.321350164925254 49 7.3 8.06153427409026 -0.76153427409026 50 6.9 7.55622209466666 -0.656222094666664 51 6.1 6.52672261166944 -0.426722611669438 52 5.8 5.22456996080117 0.575430039198834 53 6.2 5.55307599008705 0.646924009912953 54 7.1 6.58784794644136 0.512152053558637 55 7.7 7.71001599648092 -0.0100159964809237 56 7.9 8.3743139653839 -0.47431396538390 57 7.7 8.077476478256 -0.377476478256004 58 7.4 7.51232643982913 -0.112326439829127 59 7.5 6.9534346494156 0.546565350584396 60 8 8.12597042012929 -0.125970420129287 61 8.1 8.201469492428 -0.101469492427995 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 8.32230469229123 7.65032009344552 8.99428929113694 63 8.54273899730406 7.11558644588284 9.96989154872528 64 8.72780621234504 6.35683189701666 11.0987805276734 65 9.07263962095149 5.54272545821974 12.6025537836832 66 9.43853049252806 4.56621367289769 14.3108473121584 67 9.41430068676692 3.28352202385219 15.5450793496817 68 9.45944649077411 1.95968926992142 16.9592037116268 69 9.44918675329987 0.564927983776867 18.3334455228229 70 9.43631804412498 -0.874852853041075 19.7474889412910 71 9.26485419615837 -2.31506399369032 20.8447723860071 72 9.73163480068307 -4.00125198452099 23.4645215858871 73 9.82221515550887 -6.28171928080732 25.9261495918251

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/1rz3j1259940851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/1rz3j1259940851.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/2pnc31259940851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/2pnc31259940851.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/3jny31259940851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940896757ftczxhxqw1lo/3jny31259940851.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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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