*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 08:23:15 -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/t1259940228ndkpmvxj4j61x7d.htm/, Retrieved Fri, 04 Dec 2009 16:23:52 +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/t1259940228ndkpmvxj4j61x7d.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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274412 272433 268361 268586 264768 269974 304744 309365 308347 298427 289231 291975 294912 293488 290555 284736 281818 287854 316263 325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 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

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 0.897909443669848 beta 0.121731637445269 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 294912 285544.431319981 9367.56868001918 14 293488 293971.846090189 -483.846090189123 15 290555 291712.505658404 -1157.50565840380 16 284736 285260.591331686 -524.591331686475 17 281818 281804.898672166 13.1013278336031 18 287854 287956.630200848 -102.630200848449 19 316263 326853.300613778 -10590.3006137776 20 325412 321566.000273580 3845.99972641963 21 326011 323685.540423818 2325.45957618172 22 328282 315493.685833105 12788.3141668948 23 317480 318613.054615749 -1133.05461574852 24 317539 322122.483657163 -4583.48365716252 25 313737 323537.415756767 -9800.41575676686 26 312276 312473.656537743 -197.656537743344 27 309391 309133.074789482 257.925210517715 28 302950 302709.928061431 240.071938568552 29 300316 298952.964714496 1363.03528550430 30 304035 305983.45226617 -1948.45226616971 31 333476 343260.82938262 -9784.82938262017 32 337698 339616.444050717 -1918.44405071699 33 335932 334862.583022363 1069.41697763669 34 323931 324727.874595050 -796.874595049536 35 313927 311523.916559079 2403.08344092086 36 314485 315342.959249098 -857.959249098029 37 313218 317417.124090838 -4199.12409083801 38 309664 310882.84271168 -1218.84271168016 39 302963 305139.268241003 -2176.26824100252 40 298989 294904.71189283 4084.28810717002 41 298423 293447.909417953 4975.09058204654 42 301631 302391.836013607 -760.836013607448 43 329765 338698.948976348 -8933.94897634757 44 335083 335721.225426708 -638.22542670765 45 327616 331736.865112247 -4120.86511224665 46 309119 315795.872347194 -6676.87234719389 47 295916 296381.391523783 -465.391523782630 48 291413 295130.355029477 -3717.35502947686 49 291542 291699.734879385 -157.734879384516 50 284678 287281.358562566 -2603.35856256558 51 276475 278458.604235113 -1983.6042351129 52 272566 267629.5575063 4936.44249369996 53 264981 265575.522763335 -594.522763334506 54 263290 266025.682297671 -2735.68229767052 55 296806 292139.159990631 4666.84000936855 56 303598 299956.635784707 3641.36421529332 57 286994 298621.921577478 -11627.9215774777 58 276427 275170.902420806 1256.09757919359 59 266424 263712.810092928 2711.18990707211 60 267153 264286.453735383 2866.54626461701 61 268381 267008.206253153 1372.79374684725 62 262522 264147.859129584 -1625.85912958387 63 255542 256921.976843391 -1379.97684339058 64 253158 248171.487665143 4986.51233485743 65 243803 246367.213856235 -2564.21385623497 66 250741 244791.075928556 5949.92407144394 67 280445 279121.020830441 1323.97916955902 68 285257 284429.313356364 827.686643635912 69 270976 279838.082179015 -8862.08217901486 70 261076 261515.848421809 -439.848421808711 71 255603 249880.152477315 5722.84752268463 72 260376 254134.163854508 6241.83614549204 73 263903 261036.740957824 2866.25904217645 74 264291 260761.255380406 3529.74461959425 75 263276 260204.073712558 3071.92628744247 76 262572 258423.578484320 4148.4215156796 77 256167 257220.283077732 -1053.28307773196 78 264221 260550.951310324 3670.04868967616 79 293860 296457.037692250 -2597.03769225033 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 80 300597.60195908 291690.357497741 309504.846420420 81 295981.006901015 283459.160170707 308502.853631322 82 288674.578714217 273015.343944749 304333.813483685 83 279975.611404529 261459.463553877 298491.75925518 84 281394.657842215 259522.52264454 303266.793039889 85 284019.163037638 258665.327653885 309372.998421391 86 282266.188694958 253754.518724470 310777.858665446 87 279051.090073625 247517.40376877 310584.776378479 88 274805.233219444 240374.146123622 309236.320315265 89 269077.783282806 231963.718660532 306191.847905080 90 274176.786930806 232878.063182934 315475.510678677 91 307014.564577500 257793.98058216 356235.148572839

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/14u8x1259940194.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/14u8x1259940194.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/2f0621259940194.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/2f0621259940194.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/34d9z1259940194.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259940228ndkpmvxj4j61x7d/34d9z1259940194.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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