*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 14:23:08 +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/t1305814777q64bk2rqxgygeln.htm/, Retrieved Thu, 19 May 2011 16:19:37 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

30790 30800 31025 30835 31110 31270 31090 30755 31460 32135 32680 32700 32515 32275 32200 31835 31985 31875 31795 32260 33255 33160 32195 33130 33950 34210 33855 33735 34175 34265 33915 33660 33720 33810 33590 33545 33660 33165 33800 33880 33975 33930 33905 33890 33640 34395 34245 33940 34295 33745 33535 33715 33600 34120 34330 34130 33755 32910 32910 32850 32780 32565 31905 31975 31380 31355 31440 30310 31410 31300 31070 31075 31815

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 0.881100620755513 beta 0.0267387813206933 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 32515 32055.3766025641 459.623397435891 14 32275 32222.8914167431 52.108583256886 15 32200 32152.1556636433 47.8443363566985 16 31835 31808.7898713136 26.2101286864054 17 31985 32056.9796641921 -71.9796641920693 18 31875 31981.7502272917 -106.75022729173 19 31795 32092.1194376148 -297.119437614838 20 32260 31448.3792162767 811.620783723261 21 33255 32863.5887848533 391.411215146742 22 33160 33907.5645831395 -747.564583139458 23 32195 33812.8758082572 -1617.87580825716 24 33130 32404.6971689743 725.3028310257 25 33950 32934.9147665385 1015.08523346148 26 34210 33548.7725819275 661.227418072456 27 33855 34033.9538569078 -178.953856907829 28 33735 33502.5695378428 232.430462157194 29 34175 33940.029744796 234.970255204033 30 34265 34157.5957337773 107.404266222708 31 33915 34465.5430650265 -550.543065026504 32 33660 33755.8903486605 -95.8903486604904 33 33720 34325.6987745448 -605.698774544828 34 33810 34336.3754933537 -526.37549335372 35 33590 34318.9868820909 -728.986882090918 36 33545 33979.442925989 -434.442925989046 37 33660 33501.7712817191 158.228718280901 38 33165 33277.9001721621 -112.900172162139 39 33800 32922.1833689154 877.816631084643 40 33880 33336.8138214624 543.186178537573 41 33975 34021.6846282736 -46.684628273586 42 33930 33942.5827088857 -12.5827088857113 43 33905 34030.4189738699 -125.418973869855 44 33890 33723.2560802956 166.74391970443 45 33640 34443.8981610928 -803.898161092802 46 34395 34264.7456199613 130.254380038728 47 34245 34792.6663919014 -547.666391901395 48 33940 34643.0197186921 -703.0197186921 49 34295 33987.9602289324 307.039771067561 50 33745 33855.2625387277 -110.262538727693 51 33535 33612.0204754608 -77.0204754607548 52 33715 33115.415575171 599.584424828994 53 33600 33751.0319242677 -151.031924267707 54 34120 33552.7741438355 567.225856164521 55 34330 34120.4538755588 209.546124441207 56 34130 34133.4484960053 -3.4484960053378 57 33755 34574.9971061925 -819.99710619248 58 32910 34478.6225611835 -1568.62256118354 59 32910 33374.9252882213 -464.925288221333 60 32850 33227.5276239975 -377.527623997521 61 32780 32934.840502046 -154.840502046041 62 32565 32290.1667711452 274.833228854844 63 31905 32343.8619143012 -438.861914301157 64 31975 31554.0380022025 420.961997797469 65 31380 31883.9657387138 -503.965738713814 66 31355 31392.7667319746 -37.7667319745924 67 31440 31303.2344358661 136.765564133904 68 30310 31143.4376687478 -833.437668747774 69 31410 30653.7015411162 756.298458883797 70 31300 31791.4340804147 -491.434080414667 71 31070 31727.6984356857 -657.698435685656 72 31075 31375.9193781966 -300.919378196639 73 31815 31134.0936646679 680.906335332125 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 31253.4592308862 30180.9560361761 32325.9624255963 75 30950.2400869608 29503.9863156785 32396.493858243 76 30629.7689525509 28874.0049266395 32385.5329784622 77 30449.3345428289 28418.3958319876 32480.2732536703 78 30440.0051083299 28155.5049262772 32724.5052903827 79 30387.7849268558 27864.5585533764 32911.0113003351 80 29972.1892800534 27220.9750552821 32723.4035048247 81 30405.5115664701 27434.3597474935 33376.6633854467 82 30710.3937112847 27525.4857836335 33895.3016389359 83 31053.3494518788 27659.5105116035 34447.1883921541 84 31332.4420271127 27733.4792905078 34931.4047637175 85 31488.5368838715 27687.473150946 35289.600616797

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/1pv8x1305814984.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/1pv8x1305814984.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/2mnqe1305814984.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/2mnqe1305814984.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/36ezb1305814984.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305814777q64bk2rqxgygeln/36ezb1305814984.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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