Exponential smoothing Brutoschuld/Samira Allouch

*Unverified author*

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 12:28:21 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244.htm/, Retrieved Sun, 07 Jun 2009 20:29:16 +0200

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/Jun/07/t12443993569d804ty2o7q3244.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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260288 261544 259886 257006 259670 258873 264416 263596 262586 260237 261690 259295 264170 264451 265538 261723 266189 265073 267007 266376 267406 262742 260300 263074 265940 264771 268403 264264 264118 266817 269296 269001 266707 267507 267510 267420 270845 270671 273653 271567 268372 268160 267879 271142 271323 269478 271008 269145 271684 273582 279475 276188 278422 281084 278618 280738 288897 282129 286406 284288 286139 288275 287670 286864 288798 288316 286915 288006 293338 303730 306248 305700 314849

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.75041612949919 beta 0.0902646656756738 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 259886 262800 -2914 4 257006 261671.904516749 -4665.90451674876 5 259670 258913.101633601 756.898366398615 6 258873 260274.926815015 -1401.92681501515 7 264416 259921.773759202 4494.2262407981 8 263596 264297.610241472 -701.610241472023 9 262586 264726.882907059 -2140.88290705887 10 260237 263931.087174355 -3694.08717435523 11 261690 261719.518992711 -29.5189927108877 12 259295 262255.902381930 -2960.90238192963 13 264170 260391.968529636 3778.03147036358 14 264451 263840.948306046 610.051693954272 15 265538 264953.947459094 584.052540906356 16 261723 266086.997846907 -4363.99784690654 17 266189 263211.351389563 2977.64861043659 18 265073 266046.689038944 -973.68903894379 19 267007 265850.925322949 1156.07467705081 20 266376 267331.678596359 -955.678596358513 21 267406 267163.004248135 242.995751865325 22 262742 267910.294039917 -5168.29403991741 23 260300 264246.784809956 -3946.78480995598 24 263074 261232.576151664 1841.4238483363 25 265940 262686.663429665 3253.33657033514 26 264771 265420.640992233 -649.640992233355 27 268403 265181.757116869 3221.24288313149 28 264264 268065.841241574 -3801.84124157444 29 264118 265422.168009842 -1304.16800984152 30 266817 264564.449853489 2252.55014651071 31 269296 266528.329243982 2767.67075601837 32 269001 269066.234563773 -65.2345637732651 33 266707 269473.863305855 -2766.86330585508 34 267507 267666.729842166 -159.729842166358 35 267510 267805.211911047 -295.211911046703 36 267420 267822.029558153 -402.02955815295 37 270845 267731.457621262 3113.54237873817 38 270671 270489.926666867 181.073333133303 39 273653 271060.088835740 2592.91116426029 40 271567 273615.766603738 -2048.76660373819 41 268372 272549.479126951 -4177.47912695119 42 268160 269602.805456513 -1442.80545651302 43 267879 268610.545058807 -731.5450588073 44 271142 268102.473955052 3039.52604494797 45 271323 270630.160954777 692.83904522279 46 269478 271443.786366885 -1965.78636688541 47 271008 270129.181762099 878.818237901316 48 269145 271008.742020603 -1863.74202060321 49 271684 269703.998281719 1980.00171828072 50 273582 271417.779359418 2164.22064058227 51 279475 273416.397069200 6058.60293080035 52 276188 278747.807961977 -2559.80796197668 53 278422 277438.433001782 983.56699821842 54 281084 278854.686718815 2229.31328118459 55 278618 281356.773440358 -2738.77344035765 56 280738 279945.214028354 792.785971645731 57 288897 281237.493960375 7659.50603962463 58 282129 288201.496156853 -6072.49615685252 59 286406 284449.455444387 1956.54455561255 60 284288 286855.065008422 -2567.06500842172 61 286139 285692.202119926 446.797880073835 62 288275 286821.254883537 1453.74511646305 63 287670 288804.408062844 -1134.40806284419 64 286864 288768.529016988 -1904.52901698783 65 288798 288025.733491716 772.266508283501 66 288316 289343.958795330 -1027.95879532956 67 286915 289241.636114665 -2326.63611466473 68 288006 288007.167860659 -1.16786065918859 69 293338 288517.689386817 4820.31061318319 70 303730 292972.834981738 10757.1650182616 71 306248 302611.739867087 3636.26013291255 72 305700 307153.308808186 -1453.30880818627 73 314849 307777.141709535 7071.85829046485 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 315277.417333265 309182.784873738 321372.049792793 75 317470.856430298 309596.334192698 325345.378667898 76 319664.295527331 310116.569895423 329212.021159239 77 321857.734624364 310680.154881908 333035.314366821 78 324051.173721397 311257.166366084 336845.18107671 79 326244.61281843 311831.253670205 340657.971966655 80 328438.051915463 312392.677711358 344483.426119568 81 330631.491012496 312935.31035912 348327.671665872 82 332824.930109529 313455.157206776 352194.703012282 83 335018.369206562 313949.559027087 356087.179386036 84 337211.808303594 314416.728983543 360006.887623646 85 339405.247400627 314855.469600057 363955.025201198

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/1qao21244399296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/1qao21244399296.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/2em7f1244399296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/2em7f1244399296.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/3jw2k1244399296.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12443993569d804ty2o7q3244/3jw2k1244399296.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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Software written by Ed van Stee & Patrick Wessa

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