*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 07:33:11 -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/t1259937249ucvtvexbopqk74x.htm/, Retrieved Fri, 04 Dec 2009 15:34:13 +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/t1259937249ucvtvexbopqk74x.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:

WS9,ES

Dataseries X:

» Textbox « » Textfile « » CSV «

1.3 1.2 1.1 1.4 1.2 1.5 1.1 1.3 1.5 1.1 1.4 1.3 1.5 1.6 1.7 1.1 1.6 1.3 1.7 1.6 1.7 1.9 1.8 1.9 1.6 1.5 1.6 1.6 1.7 2 2 1.9 1.7 1.8 1.9 1.7 2 2.1 2.4 2.5 2.5 2.6 2.2 2.5 2.8 2.8 2.9 3 3.1 2.9 2.7 2.2 2.5 2.3 2.6 2.3 2.2 1.8 1.8

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 0.553341713987221 beta 0 gamma 0.844083465078655 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.5 1.41893876910371 0.0810612308962884 14 1.6 1.54887584608295 0.0511241539170475 15 1.7 1.68136239390808 0.0186376060919151 16 1.1 1.08280563043064 0.0171943695693588 17 1.6 1.56375566213877 0.0362443378612345 18 1.3 1.27387321470486 0.0261267852951392 19 1.7 1.36491384724107 0.335086152758934 20 1.6 1.82246058015649 -0.222460580156485 21 1.7 1.92866313091967 -0.228663130919671 22 1.9 1.32986489075222 0.57013510924778 23 1.8 2.11355119233864 -0.313551192338636 24 1.9 1.81445622294131 0.0855437770586895 25 1.6 2.19470352895315 -0.594703528953154 26 1.5 1.95022904457696 -0.45022904457696 27 1.6 1.79708414577162 -0.197084145771615 28 1.6 1.08250573695895 0.517494263041052 29 1.7 1.95840018769848 -0.258400187698482 30 2 1.45588632182518 0.544113678174821 31 2 1.98956097184463 0.0104390281553715 32 1.9 2.05727768595704 -0.157277685957041 33 1.7 2.23381218056110 -0.533812180561104 34 1.8 1.69559181661626 0.104408183383736 35 1.9 1.87207458653634 0.0279254134636573 36 1.7 1.91157141539358 -0.211571415393579 37 2 1.83074270791164 0.169257292088362 38 2.1 2.05386497901739 0.0461350209826064 39 2.4 2.32265111717495 0.077348882825051 40 2.5 1.8029790458527 0.697020954147298 41 2.5 2.58360963788585 -0.0836096378858513 42 2.6 2.39017044505937 0.209829554940633 43 2.2 2.53986759559519 -0.339867595595188 44 2.5 2.34313315453827 0.156866845461731 45 2.8 2.53907562490880 0.260924375091197 46 2.8 2.66520817257876 0.134791827421243 47 2.9 2.86413366372172 0.0358663362782807 48 3 2.76337592284359 0.236624077156410 49 3.1 3.1752437055419 -0.0752437055418973 50 2.9 3.24921777324037 -0.349217773240373 51 2.7 3.41375905686105 -0.71375905686105 52 2.2 2.53962118754568 -0.339621187545684 53 2.5 2.44868127014259 0.0513187298574125 54 2.3 2.43760728189445 -0.137607281894450 55 2.6 2.19540617847323 0.404593821526769 56 2.3 2.60922356027274 -0.309223560272744 57 2.2 2.57877530788985 -0.378775307889845 58 1.8 2.31551823875185 -0.515518238751847 59 1.8 2.10019434842643 -0.300194348426426 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 1.90935052329672 1.33464623585302 2.48405481074042 61 2.02264668970715 1.34575824426485 2.69953513514946 62 2.03389952170057 1.27776359334414 2.79003545005699 63 2.17063004510033 1.31705579025328 3.02420429994738 64 1.90039992486478 1.05435390254632 2.74644594718325 65 2.11267824041330 1.1449013696028 3.08045511122381 66 2.02119494632359 1.03284060000782 3.00954929263936 67 2.04535069926650 0.999331002665473 3.09137039586754 68 1.98048045358057 0.91401774264963 3.04694316451151 69 2.07074736656975 0.922821646960254 3.21867308617925 70 1.94899880761724 0.814580887873234 3.08341672736124 71 2.09768248461301 -19.8481061927748 24.0434711620008

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/1hr331259937189.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/1hr331259937189.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/2qwkc1259937189.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/2qwkc1259937189.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/3q42m1259937189.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937249ucvtvexbopqk74x/3q42m1259937189.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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