exponential smoothing eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 08:38:48 -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/02/t1243953632glao4q35rkrjviz.htm/, Retrieved Tue, 02 Jun 2009 16:40:36 +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/02/t1243953632glao4q35rkrjviz.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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310.95 312.97 315.07 315.43 315.73 315.77 315.77 315.77 313.99 314.57 314.63 314.65 314.65 314.93 315.27 316.26 316.98 317.01 317.07 317.07 317 317.08 317.04 317 317.05 321.59 325.59 326.23 326.28 326.35 326.35 326.35 326.39 326.74 326.9 326.9 326.91 336.93 348.5 349.43 349.26 349.26 349.28 349.61 349.66 349.68 349.91 349.91 350.89 355.52 356.36 357.04 360.28 360.63 360.79 360.97 361 361.01 361 361 361.58 363.19 363.61 364.14 365.51 365.51 365.5 365.5 364.59 364.63 364.54 363.67 365.22 369.05 370.45 370.46 370.46 370.58 370.58 370.22 370.21 370.29 370.29 370.2 370.2 372.55 374.51 375.58 375.75 375.75 375.75 375.69 375.76 377.5 377.51 377.74

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.936452106375678 beta 0.0510905500579434 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 314.65 314.062847222222 0.58715277777776 14 314.93 314.944605086629 -0.0146050866285918 15 315.27 315.250896767763 0.0191032322372280 16 316.26 316.189251980674 0.0707480193264018 17 316.98 316.934354921089 0.0456450789106384 18 317.01 316.974800663199 0.0351993368010994 19 317.07 317.521731873344 -0.451731873343817 20 317.07 317.008979399313 0.0610206006868452 21 317 315.345147853634 1.65485214636630 22 317.08 317.660121052635 -0.580121052634752 23 317.04 317.290643665247 -0.250643665247367 24 317 317.160630979219 -0.160630979218752 25 317.05 317.12245464656 -0.0724546465602316 26 321.59 317.365331949859 4.22466805014091 27 325.59 321.863515789339 3.72648421066077 28 326.23 326.674186844677 -0.444186844676494 29 326.28 327.308095438622 -1.02809543862173 30 326.35 326.663611653322 -0.313611653322425 31 326.35 327.157507009326 -0.807507009326116 32 326.35 326.631703231131 -0.281703231131246 33 326.39 325.019345371704 1.37065462829599 34 326.74 327.183689765782 -0.443689765782096 35 326.9 327.226975135375 -0.326975135375335 36 326.9 327.291613605373 -0.391613605373038 37 326.91 327.292097232676 -0.382097232676358 38 336.93 327.752628392116 9.17737160788408 39 348.5 337.328626011022 11.1713739889783 40 349.43 349.673737268367 -0.243737268367397 41 349.26 351.295536257096 -2.03553625709628 42 349.26 350.542121612269 -1.28212161226890 43 349.28 350.840415796707 -1.56041579670750 44 349.61 350.349688692796 -0.73968869279588 45 349.66 349.098267426951 0.561732573048914 46 349.68 351.035909528238 -1.35590952823844 47 349.91 350.834829874594 -0.924829874593968 48 349.91 350.909362827614 -0.99936282761422 49 350.89 350.886110547945 0.00388945205457958 50 355.52 352.878838337511 2.64116166248863 51 356.36 356.711240044503 -0.351240044503186 52 357.04 357.239819596813 -0.199819596812972 53 360.28 358.490232274139 1.78976772586083 54 360.63 361.251278741752 -0.621278741752121 55 360.79 362.066722110706 -1.27672211070580 56 360.97 361.823375530047 -0.853375530047117 57 361 360.472314844537 0.527685155463473 58 361.01 362.178702372381 -1.16870237238078 59 361 362.111775488561 -1.11177548856091 60 361 361.929010247339 -0.92901024733942 61 361.58 361.961264129234 -0.381264129234182 62 363.19 363.668349669231 -0.47834966923125 63 363.61 364.147510690169 -0.537510690168517 64 364.14 364.260560345816 -0.120560345815932 65 365.51 365.464702858521 0.0452971414790682 66 365.51 366.108530313146 -0.598530313145659 67 365.5 366.574323887690 -1.07432388769041 68 365.5 366.227799280841 -0.727799280841396 69 364.59 364.768489235643 -0.178489235642758 70 364.63 365.358381309089 -0.728381309088775 71 364.54 365.381083148135 -0.841083148135226 72 363.67 365.150045182103 -1.48004518210251 73 365.22 364.361348232872 0.858651767128322 74 369.05 366.942967280499 2.10703271950075 75 370.45 369.682731418725 0.767268581274834 76 370.46 370.949842247384 -0.489842247384161 77 370.46 371.706743530168 -1.24674353016763 78 370.58 370.925940384150 -0.345940384150424 79 370.58 371.43633901222 -0.85633901222036 80 370.22 371.164699308334 -0.944699308333838 81 370.21 369.375534537074 0.834465462926005 82 370.29 370.765883609822 -0.47588360982212 83 370.29 370.916773870737 -0.626773870736827 84 370.2 370.7549733532 -0.554973353200239 85 370.2 370.934591898066 -0.73459189806573 86 372.55 371.980730389782 0.569269610218157 87 374.51 372.998925174157 1.51107482584308 88 375.58 374.721886076732 0.858113923267638 89 375.75 376.596673584464 -0.846673584463588 90 375.75 376.170591123898 -0.420591123898419 91 375.75 376.497906772331 -0.747906772331476 92 375.69 376.246639993924 -0.556639993924477 93 375.76 374.876949048279 0.883050951721032 94 377.5 376.17486338747 1.32513661252989 95 377.51 378.034239024749 -0.524239024749477 96 377.74 378.009430867254 -0.269430867253845 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 378.495103963035 374.747881657762 382.242326268308 98 380.397228013070 375.139301533829 385.655154492312 99 381.000160533465 374.472943356632 387.527377710299 100 381.25226402429 373.572271941374 388.932256107205 101 382.159763891063 373.39373756367 390.925790218457 102 382.538766066849 372.727972757363 392.349559376335 103 383.244406371056 372.415191001902 394.073621740209 104 383.746717239580 371.915900624742 395.577533854417 105 383.057458291688 370.235410955174 395.879505628202 106 383.581958735416 369.774489103352 397.38942836748 107 384.044911248571 369.254493244106 398.835329253035 108 384.514329740868 368.740936860126 400.287722621609

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/18t3o1243953526.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/18t3o1243953526.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/250k41243953526.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/250k41243953526.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/372ok1243953526.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243953632glao4q35rkrjviz/372ok1243953526.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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