workshop 9

*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 04:59:12 -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/t1259928012wvemfjci7ka8nbb.htm/, Retrieved Fri, 04 Dec 2009 13:00:16 +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/t1259928012wvemfjci7ka8nbb.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:

» Textbox « » Textfile « » CSV «

0.6348 0.634 0.62915 0.62168 0.61328 0.6089 0.60857 0.62672 0.62291 0.62393 0.61838 0.62012 0.61659 0.6116 0.61573 0.61407 0.62823 0.64405 0.6387 0.63633 0.63059 0.62994 0.63709 0.64217 0.65711 0.66977 0.68255 0.68902 0.71322 0.70224 0.70045 0.69919 0.69693 0.69763 0.69278 0.70196 0.69215 0.6769 0.67124 0.66532 0.67157 0.66428 0.66576 0.66942 0.6813 0.69144 0.69862 0.695 0.69867 0.68968 0.69233 0.68293 0.68399 0.66895 0.68756 0.68527 0.6776 0.68137 0.67933 0.67922

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.66962132181715 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.61659 0.612497500972189 0.00409249902781061 14 0.6116 0.609477852953774 0.00212214704622571 15 0.61573 0.615158227348706 0.000571772651294267 16 0.61407 0.614161909656626 -9.1909656625977e-05 17 0.62823 0.6280860151228 0.000143984877200243 18 0.64405 0.643136853854259 0.00091314614574145 19 0.6387 0.615711816060138 0.0229881839398619 20 0.63633 0.652568374770993 -0.0162383747709927 21 0.63059 0.640196745644255 -0.00960674564425479 22 0.62994 0.636568216833885 -0.00662821683388526 23 0.63709 0.627053517654655 0.0100364823453450 24 0.64217 0.634272190935844 0.0078978090641565 25 0.65711 0.635381124861123 0.021728875138877 26 0.66977 0.643126410940054 0.026643589059946 27 0.68255 0.664948883103742 0.0176011168962579 28 0.68902 0.674894868952347 0.0141251310476532 29 0.71322 0.699928321453581 0.0132916785464188 30 0.70224 0.725875451407125 -0.0236354514071250 31 0.70045 0.686888437618467 0.0135615623815333 32 0.69919 0.70505955943636 -0.00586955943635947 33 0.69693 0.701769731679134 -0.00483973167913399 34 0.69763 0.702615579996933 -0.00498557999693339 35 0.69278 0.699619890729639 -0.00683989072963931 36 0.70196 0.694710478407869 0.00724952159213132 37 0.69215 0.699737775508837 -0.00758777550883682 38 0.6769 0.688879878046408 -0.0119798780464085 39 0.67124 0.681751226894113 -0.0105112268941132 40 0.66532 0.671704469979952 -0.00638446997995168 41 0.67157 0.682223139164555 -0.0106531391645552 42 0.66428 0.679558931514768 -0.0152789315147677 43 0.66576 0.658950519108131 0.00680948089186895 44 0.66942 0.666074695202517 0.00334530479748285 45 0.6813 0.669282977878984 0.0120170221210159 46 0.69144 0.68127125354148 0.0101687464585204 47 0.69862 0.687811360464139 0.0108086395358614 48 0.695 0.699369288308636 -0.00436928830863603 49 0.69867 0.691740156022961 0.00692984397703855 50 0.68968 0.689056241671674 0.000623758328326174 51 0.69233 0.690825445932794 0.00150455406720562 52 0.68293 0.690097840493339 -0.00716784049333918 53 0.68399 0.69901943908038 -0.0150294390803799 54 0.66895 0.691871173926501 -0.0229211739265007 55 0.68756 0.673354598081097 0.0142054019189030 56 0.68527 0.684297402998745 0.000972597001255071 57 0.6776 0.688802500116735 -0.0112025001167348 58 0.68137 0.684598615739255 -0.00322861573925481 59 0.67933 0.682354259245283 -0.00302425924528293 60 0.67922 0.679669736423884 -0.000449736423883906 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 0.678424441319921 0.655843630819011 0.701005251820831 62 0.669313770075471 0.642260794643202 0.69636674550774 63 0.670932101888988 0.639923480247097 0.70194072353088 64 0.666483927742407 0.632140305001961 0.700827550482853 65 0.677289834037542 0.63940654137935 0.715173126695734 66 0.677433546186646 0.636673722185749 0.718193370187543 67 0.686569538829388 0.642707126635386 0.73043195102339 68 0.683633434893761 0.63743344436689 0.729833425420631 69 0.683426662890744 0.634874514509401 0.731978811272087 70 0.689398792834897 0.638241194377664 0.740556391292131 71 0.689370561464864 0.636081682416199 0.742659440513529 72 0.689551747635884 -25.9473178257186 27.3264213209903

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/11h531259927949.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/11h531259927949.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/2g9gm1259927949.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/2g9gm1259927949.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/3jieo1259927949.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928012wvemfjci7ka8nbb/3jieo1259927949.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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