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 05:15:07 -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/t1259928958haptvd4bitxhx6n.htm/, Retrieved Fri, 04 Dec 2009 13:16:03 +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/t1259928958haptvd4bitxhx6n.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 «

130 136.7 138.1 139.5 140.4 144.6 151.4 147.9 141.5 143.8 143.6 150.5 150.1 154.9 162.1 176.7 186.6 194.8 196.3 228.8 267.2 237.2 254.7 258.2 257.9 269.6 266.9 269.6 253.9 258.6 274.2 301.5 304.5 285.1 287.7 265.5 264.1 276.1 258.9 239.1 250.1 276.8 297.6 295.4 283 275.8 279.7 254.6 234.6 176.9 148.1 122.7 124.9 121.6 128.4 144.5 151.8 167.1 173.8 203.7 199.8

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.91594433817239 beta 0.254681260792864 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 150.1 130.88058478487 19.2194152151301 14 154.9 157.905109673890 -3.00510967389044 15 162.1 163.119940761206 -1.01994076120627 16 176.7 176.837042114557 -0.137042114557289 17 186.6 187.219177521515 -0.619177521514899 18 194.8 194.736387791569 0.0636122084314081 19 196.3 222.232225112377 -25.9322251123766 20 228.8 195.117517157823 33.6824828421766 21 267.2 224.202594102331 42.9974058976687 22 237.2 283.901442079443 -46.7014420794433 23 254.7 244.789504495632 9.91049550436773 24 258.2 271.28539781617 -13.0853978161700 25 257.9 263.814699897086 -5.91469989708571 26 269.6 262.399814808797 7.20018519120333 27 266.9 276.905536256762 -10.0055362567618 28 269.6 284.382714022403 -14.7827140224032 29 253.9 276.767504829663 -22.8675048296630 30 258.6 253.209197207961 5.39080279203932 31 274.2 278.157364936914 -3.95736493691419 32 301.5 270.011846774133 31.4881532258671 33 304.5 288.32979416855 16.1702058314501 34 285.1 302.837171801158 -17.7371718011576 35 287.7 290.070933366641 -2.37093336664128 36 265.5 296.128872327679 -30.6288723276792 37 264.1 261.449956109600 2.6500438904003 38 276.1 259.405421606030 16.6945783939705 39 258.9 273.855365360832 -14.9553653608322 40 239.1 267.417240107409 -28.3172401074092 41 250.1 234.472683992849 15.6273160071509 42 276.8 245.502094112041 31.2979058879588 43 297.6 297.851825910214 -0.251825910213597 44 295.4 299.929471940812 -4.52947194081179 45 283 280.144564306973 2.8554356930274 46 275.8 273.468688520899 2.33131147910086 47 279.7 278.113449979531 1.58655002046862 48 254.6 283.769198230010 -29.1691982300104 49 234.6 252.186511999984 -17.586511999984 50 176.9 227.075627290153 -50.1756272901533 51 148.1 158.405168445699 -10.3051684456992 52 122.7 131.101893376469 -8.4018933764694 53 124.9 101.292938655341 23.6070613446595 54 121.6 104.767825624628 16.8321743753722 55 128.4 111.614796694672 16.7852033053279 56 144.5 114.106816448153 30.3931835518466 57 151.8 128.823794911813 22.9762050881868 58 167.1 143.993622153862 23.1063778461379 59 173.8 170.613931009588 3.18606899041225 60 203.7 178.801986795766 24.8980132042344 61 199.8 213.502594383305 -13.7025943833049 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 205.237717295804 164.921283817349 245.554150774259 63 213.526101489112 152.16778895417 274.884414024055 64 228.756986518236 143.997795658477 313.516177377995 65 248.064929318224 136.535302367125 359.594556269323 66 258.946715255600 122.318556216615 395.574874294584 67 285.912727856994 113.677834705983 458.147621008005 68 297.236700587116 96.2403909860852 498.233010188147 69 288.655223364216 72.0672682197685 505.243178508664 70 285.761732983868 50.2384250387331 521.285040929004 71 291.659694904361 29.9406821266919 553.378707682029 72 301.529738208398 9.14505609709352 593.914420319703 73 305.301865648701 -10.1412613150731 620.744992612474

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/18nai1259928904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/18nai1259928904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/2i1xe1259928904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/2i1xe1259928904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/3yhf71259928904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928958haptvd4bitxhx6n/3yhf71259928904.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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