*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 14:53:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2.htm/, Retrieved Thu, 19 May 2011 16:54:59 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

12544 12264 13783 11214 11453 10883 10381 10348 10024 10805 10796 11907 12261 11377 12689 11474 10992 10764 12164 10409 10398 10349 10865 11630 12221 10884 12019 11021 10799 10423 10484 10450 9906 11049 11281 12485 12849 11380 12079 11366 11328 10444 10854 10434 10137 10992 10906 12367 14371 11695 11546 10922 10670 10254 10573 10239 10253 11176 10719 11817 12503 11510 12012 10941 11252 10662 11114 10415 10626 11411 10936 12513

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.000665490790061819 beta 0.502252609509736 gamma 0.291292247840986 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 12261 12392.7409188034 -131.740918803423 14 11377 11435.3280356034 -58.3280356034284 15 12689 12732.6528455101 -43.6528455101361 16 11474 11524.5144975645 -50.5144975644507 17 10992 11062.0630323936 -70.063032393582 18 10764 10846.1168063372 -82.1168063372479 19 12164 10403.968444849 1760.03155515101 20 10409 10424.8842969716 -15.8842969715643 21 10398 10187.4046508786 210.595349121379 22 10349 11007.3544485718 -658.354448571823 23 10865 11010.1309168334 -145.130916833421 24 11630 12148.9920880866 -518.992088086612 25 12221 12398.5814178402 -177.581417840202 26 10884 11462.5585402414 -578.558540241409 27 12019 12763.6853211715 -744.685321171455 28 11021 11552.7249657691 -531.724965769115 29 10799 11083.7438094974 -284.743809497388 30 10423 10863.5552223976 -440.555222397581 31 10484 10956.7042910348 -472.704291034797 32 10450 10457.7112784433 -7.71127844331022 33 9906 10284.7109203862 -378.710920386213 34 11049 10849.6676632752 199.332336724841 35 11281 11001.0491529082 279.950847091808 36 12485 12030.1405983684 454.859401631551 37 12849 12378.8653934484 470.13460655163 38 11380 11325.8695412341 54.1304587658724 39 12079 12578.5893776035 -499.589377603535 40 11366 11429.397717153 -63.3977171530241 41 11328 11032.393750559 295.60624944104 42 10444 10767.198611474 -323.198611473972 43 10854 10851.0701460534 2.9298539466381 44 10434 10487.914270091 -53.9142700910488 45 10137 10207.0322073474 -70.0322073474053 46 10992 10940.71145542 51.2885445799839 47 10906 11115.6624771192 -209.662477119176 48 12367 12195.3801732874 171.619826712631 49 14371 12548.3048756908 1822.69512430924 50 11695 11375.5048989919 319.495101008126 51 11546 12467.6969727165 -921.696972716512 52 10922 11445.5406044865 -523.540604486499 53 10670 11152.923603917 -482.92360391695 54 10254 10707.0047471266 -453.004747126577 55 10573 10885.6094718567 -312.609471856727 56 10239 10505.4750087136 -266.475008713622 57 10253 10219.4671704639 33.532829536065 58 11176 10988.2738197706 187.72618022936 59 10719 11087.1410226828 -368.141022682825 60 11817 12277.4787561014 -460.478756101396 61 12503 13110.1317336603 -607.131733660295 62 11510 11496.8470192956 13.1529807043698 63 12012 12226.1352154643 -214.135215464286 64 10941 11319.1979131589 -378.197913158865 65 11252 11037.3952706309 214.604729369104 66 10662 10599.7771788511 62.2228211489019 67 11114 10818.893069249 295.106930751033 68 10415 10452.0952769259 -37.0952769258656 69 10626 10253.1511309988 372.848869001227 70 11411 11066.7616853704 344.238314629611 71 10936 11003.6659644645 -67.6659644644733 72 12513 12167.169697048 345.830302952012 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 12957.7837255754 12030.3612834795 13885.2061676713 74 11525.7847735304 10598.3618679689 12453.2076790919 75 12189.2144275895 11261.7906968537 13116.6381583253 76 11235.0462560533 10307.6212348248 12162.4712772818 77 11126.5706232492 10199.1437426009 12053.9975038974 78 10644.8912789482 9717.46186634614 11572.3206915502 79 10932.1768475878 10004.7441268938 11859.6095682819 80 10468.7993931146 9541.362484589 11396.2363016403 81 10389.5466742235 9462.10459452987 11316.9887539171 82 11194.7886492887 10267.3403114989 12122.2369870784 83 11011.6521410937 10084.1963546943 11939.1079274931 84 12295.6845966289 11368.2200675287 13223.1491257292

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/1v1vn1305816826.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/1v1vn1305816826.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/2pdis1305816826.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/2pdis1305816826.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/3y1dz1305816826.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581689658inyx5dcixzoh2/3y1dz1305816826.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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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