Workshop 8 - blog 2

*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, 30 Nov 2010 19:48:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e.htm/, Retrieved Tue, 30 Nov 2010 20:56:34 +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/2010/Nov/30/t129114699062lxe92rvy7ef0e.htm/}, year = {2010}, } @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 = {2010}, 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 «

219,3 211,1 215,2 240,2 242,2 240,7 255,4 253 218,2 203,7 205,6 215,6 188,5 202,9 214 230,3 230 241 259,6 247,8 270,3 289,7 322,7 315 320,2 329,5 360,6 382,2 435,4 464 468,8 403 351,6 252 188 146,5 152,9 148,1 165,1 177 206,1 244,9 228,6 253,4 241,1 261,4 273,7 263,7 272,5 263,2 279,8 298,1 267,6 264,3 264,3 268,7 269,1 288,6

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 188.5 190.796474358974 -2.29647435897439 14 202.9 204.36351981352 -1.46351981351984 15 214 213.467686480186 0.532313519813528 16 230.3 225.967686480186 4.33231351981354 17 230 222.959353146853 7.04064685314682 18 241 233.401019813520 7.59898018648019 19 259.6 278.26351981352 -18.6635198135199 20 247.8 260.246853146853 -12.4468531468532 21 270.3 214.813519813520 55.4864801864803 22 289.7 257.684353146853 32.0156468531468 23 322.7 293.942686480187 28.7573135198135 24 315 334.617686480186 -19.6176864801865 25 320.2 289.134353146853 31.0656468531469 26 329.5 336.06351981352 -6.56351981351986 27 360.6 340.067686480186 20.5323135198136 28 382.2 372.567686480186 9.63231351981352 29 435.4 374.859353146853 60.5406468531468 30 464 438.80101981352 25.1989801864802 31 468.8 501.26351981352 -32.4635198135198 32 403 469.446853146853 -66.4468531468532 33 351.6 370.01351981352 -18.4135198135197 34 252 338.984353146853 -86.9843531468532 35 188 256.242686480187 -68.2426864801865 36 146.5 199.917686480186 -53.4176864801865 37 152.9 120.634353146853 32.2656468531468 38 148.1 168.76351981352 -20.6635198135199 39 165.1 158.667686480186 6.43231351981353 40 177 177.067686480186 -0.0676864801864667 41 206.1 169.659353146853 36.4406468531468 42 244.9 209.501019813520 35.3989801864802 43 228.6 282.16351981352 -53.5635198135199 44 253.4 229.246853146853 24.1531468531469 45 241.1 220.413519813520 20.6864801864803 46 261.4 228.484353146853 32.9156468531468 47 273.7 265.642686480187 8.05731351981348 48 263.7 285.617686480186 -21.9176864801865 49 272.5 237.834353146853 34.6656468531469 50 263.2 288.36351981352 -25.1635198135199 51 279.8 273.767686480186 6.03231351981356 52 298.1 291.767686480186 6.33231351981357 53 267.6 290.759353146853 -23.1593531468532 54 264.3 271.00101981352 -6.70101981351985 55 264.3 301.56351981352 -37.2635198135198 56 268.7 264.946853146853 3.7531468531468 57 269.1 235.713519813520 33.3864801864803 58 288.6 256.484353146853 32.1156468531469 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 59 292.842686480187 228.635746171010 357.049626789363 60 304.760372960373 213.958047176656 395.56269874409 61 278.894726107226 167.685043293191 390.104408921261 62 294.758245920746 166.344365302394 423.172126539098 63 305.325932400932 161.754849242343 448.897015559522 64 317.293618881119 160.0193771783 474.567860583938 65 309.952972027972 140.077375525523 479.828568530421 66 313.353991841492 131.749340274059 494.958643408925 67 350.617511655012 157.996690727483 543.23833258254 68 351.264364801865 148.224191834392 554.304537769337 69 318.277884615385 105.327554673102 531.228214557668 70 305.662237762238 83.2428721341672 528.081603390308

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/1uj1i1291146521.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/1uj1i1291146521.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/2nsil1291146521.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/2nsil1291146521.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/3nsil1291146521.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t129114699062lxe92rvy7ef0e/3nsil1291146521.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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