ws9

*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: Tue, 01 Dec 2009 14:47:16 -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/01/t1259704487m3eb71az9jkyqbt.htm/, Retrieved Tue, 01 Dec 2009 22:54:51 +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/01/t1259704487m3eb71az9jkyqbt.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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325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 310631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224

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 0.641464199430926 beta 0.149080426851784 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 337698 338129.808201150 -431.808201150445 14 335932 336292.340320842 -360.340320842166 15 323931 324279.172300144 -348.172300143982 16 313927 314044.535194918 -117.535194918106 17 314485 314074.404418508 410.595581492351 18 313218 312734.832013465 483.167986534652 19 309664 311475.27546251 -1811.27546250977 20 302963 306210.600288761 -3247.60028876114 21 298989 296942.254665062 2046.74533493759 22 298423 295531.938077474 2891.06192252599 23 310631 301168.019999867 9462.98000013281 24 329765 337962.286114488 -8197.2861144878 25 335083 336931.639738523 -1848.63973852270 26 327616 334267.265346076 -6651.26534607634 27 309119 317893.093062713 -8774.09306271316 28 295916 301385.247821761 -5469.24782176124 29 291413 296328.534686983 -4915.53468698269 30 291542 289376.459657051 2165.54034294933 31 284678 286392.666639411 -1714.66663941147 32 276475 278905.002845494 -2430.00284549355 33 272566 270458.093180198 2107.90681980172 34 264981 267591.202643675 -2610.20264367491 35 263290 268756.376123083 -5466.37612308329 36 296806 281864.786578827 14941.2134211731 37 303598 295071.472084992 8526.52791500837 38 286994 296502.935654430 -9508.93565442954 39 276427 277510.509852600 -1083.50985259959 40 266424 267345.581287227 -921.581287226756 41 267153 265141.351888260 2011.64811174042 42 268381 265544.267060637 2836.73293936258 43 262522 262427.393696742 94.6063032578095 44 255542 256872.579053333 -1330.57905333309 45 253158 251750.116090872 1407.88390912814 46 243803 247717.896494066 -3914.89649406596 47 250741 247270.440222814 3470.55977718590 48 280445 273433.001007394 7011.9989926056 49 285257 279818.680188764 5438.31981123617 50 270976 273870.314123761 -2894.31412376126 51 261076 263653.918265663 -2577.91826566315 52 255603 253905.966714528 1697.03328547216 53 260376 255554.211328954 4821.78867104626 54 263903 259474.819994835 4428.18000516525 55 264291 258088.372041888 6202.62795811243 56 263276 258092.895311786 5183.10468821405 57 262572 260848.558023756 1723.44197624366 58 256167 257641.672500395 -1474.67250039469 59 264221 264795.580508491 -574.580508490501 60 293860 294010.622286622 -150.622286622121 61 300713 297605.562911227 3107.43708877300 62 287224 288536.835335810 -1312.83533580956 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 63 281045.210151128 271896.405397039 290194.014905216 64 276320.704821048 265036.744675594 287604.664966502 65 280308.959914284 266633.598762833 293984.321065734 66 282727.645294841 266577.147055184 298878.143534497 67 280066.981204555 261571.462347718 298562.500061392 68 276019.089614769 255213.416693857 296824.762535681 69 274176.106518518 250877.545756216 297474.66728082 70 268364.756162014 242848.314389298 293881.197934729 71 277223.911670223 248121.780579891 306326.042760556 72 308524.808309352 273209.734091762 343839.882526941 73 313737.147427361 274632.855853515 352841.439001208 74 300362.909087304 260743.468607088 339982.34956752

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/149hx1259704034.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/149hx1259704034.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/21gtc1259704034.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/21gtc1259704034.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/3ib7y1259704034.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259704487m3eb71az9jkyqbt/3ib7y1259704034.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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