workshop 9 - review link 4

*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 05:15:32 -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/t12605338092cs0pfvmhr1avql.htm/, Retrieved Fri, 11 Dec 2009 13:16:53 +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/t12605338092cs0pfvmhr1avql.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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5.4 5.4 5.6 5.7 5.8 5.8 5.8 5.9 6.1 6.4 6.4 6.3 6.2 6.2 6.3 6.4 6.5 6.6 6.6 6.6 6.8 7 7.2 7.3 7.5 7.6 7.6 7.7 7.7 7.7 7.7 7.6 7.7 7.9 7.9 7.9 7.8 7.6 7.4 7 7 7.2 7.5 7.8 7.8 7.7 7.6 7.6 7.5 7.5 7.6 7.6 7.9 7.6 7.5 7.5 7.6 7.7 7.8 7.9 7.9

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 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 6.2 5.83222509765895 0.367774902341054 14 6.2 6.19877253344505 0.00122746655494854 15 6.3 6.30285764898377 -0.0028576489837695 16 6.4 6.40700240339455 -0.00700240339454616 17 6.5 6.50289753406811 -0.00289753406810789 18 6.6 6.58624201176324 0.0137579882367573 19 6.6 6.52989357772847 0.070106422271528 20 6.6 6.69937666821261 -0.0993766682126065 21 6.8 6.81497786457103 -0.0149778645710335 22 7 7.13045746695204 -0.130457466952037 23 7.2 6.99734126441402 0.202658735585979 24 7.3 7.07832022877243 0.221679771227565 25 7.5 7.16835352833736 0.331646471662637 26 7.6 7.48598564819915 0.114014351800849 27 7.6 7.71249733960818 -0.11249733960818 28 7.7 7.71657530472002 -0.0165753047200248 29 7.7 7.81140647404256 -0.111406474042564 30 7.7 7.79085739637863 -0.0908573963786266 31 7.7 7.6082034368834 0.0917965631165982 32 7.6 7.80587460308918 -0.20587460308918 33 7.7 7.83818804107117 -0.138188041071166 34 7.9 8.06569609505028 -0.165696095050285 35 7.9 7.88882199463714 0.0111780053628561 36 7.9 7.76046443057966 0.139535569420337 37 7.8 7.75257301745751 0.0474269825424853 38 7.6 7.78303482852702 -0.183034828527020 39 7.4 7.71249733960818 -0.312497339608179 40 7 7.51510255066995 -0.515102550669953 41 7 7.10682473713324 -0.106824737133241 42 7.2 7.08816508868632 0.111834911313681 43 7.5 7.11806259181298 0.381937408187021 44 7.8 7.60469316038435 0.195306839615652 45 7.8 8.0428300763712 -0.242830076371194 46 7.7 8.16961149817231 -0.469611498172314 47 7.6 7.69071516569867 -0.0907151656986738 48 7.6 7.46811691551942 0.131883084480577 49 7.5 7.46046327289744 0.0395367271025613 50 7.5 7.48598564819915 0.0140143518008493 51 7.6 7.61180879027787 -0.0118087902778656 52 7.6 7.71657530472002 -0.116575304720025 53 7.9 7.71075194019837 0.189248059801626 54 7.6 7.99162662714786 -0.391626627147859 55 7.5 7.51017526786932 -0.0101752678693172 56 7.5 7.60469316038435 -0.104693160384348 57 7.6 7.73586702342115 -0.135867023421153 58 7.7 7.96178069192826 -0.261780691928258 59 7.8 7.69071516569867 0.109284834301326 60 7.9 7.66301525889292 0.236984741107084 61 7.9 7.75257301745751 0.147426982542486 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 7.88205122196964 7.50042279105029 8.263679652889 63 7.99649062337784 7.4549252686521 8.53805597810358 64 8.11598559395485 7.45020133340086 8.78176985450883 65 8.2301148344968 7.45892703749379 9.0013026314998 66 8.32301113408503 7.45990365165187 9.18611861651818 67 8.21892984438083 7.29075639925975 9.14710328950192 68 8.32786987686483 7.31922996835364 9.33650978537602 69 8.58295190624716 7.48260253487556 9.68330127761876 70 8.98321912780065 7.7777822331166 10.1886560224847 71 8.96178752690756 7.70825678877739 10.2153182650377 72 8.79516758062428 7.51538726279329 10.0749478984553 73 8.62419692850625 2.36220320794121 14.8861906490713

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/1ss7r1260533730.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/1ss7r1260533730.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/28i381260533730.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/28i381260533730.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/3yid61260533730.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605338092cs0pfvmhr1avql/3yid61260533730.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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