Triple exponential smoothing model roomijs - Sophie Volckaerts - 2mar03

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 16:26:58 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz.htm/, Retrieved Thu, 29 May 2008 00:28:34 +0200

User-defined keywords:

Dataseries X:

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2,6900 2,7200 2,6800 2,7200 2,7000 2,7200 2,7200 2,7100 2,6800 2,6500 2,6600 2,6900 2,6700 2,6700 2,6500 2,6600 2,7600 2,7900 2,7900 2,7800 2,8100 2,8100 2,7900 2,7900 2,7900 2,8000 2,8000 2,8000 2,7700 2,7800 2,7500 2,7400 2,7400 2,7200 2,7100 2,7100 2,7000 2,6900 2,7000 2,7100 2,7600 2,7600 2,7500 2,7400 2,7100 2,7300 2,7300 2,7300 2,7200 2,7200 2,7500 2,8200 2,8500 2,8300 2,8500 2,8500 2,7900 2,8100 2,8000 2,7900 2,7900 2,8000 2,8000 2,8600 2,8600 2,8500 2,8100 2,7900 2,7800 2,7700 2,7800 2,8500 2,8200

Text written by user:

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.700557932823512 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2.67 2.64823973429952 0.0217602657004825 14 2.67 2.65765072772300 0.0123492722769951 15 2.65 2.63796877504792 0.0120312249520826 16 2.66 2.64431401179635 0.0156859882036500 17 2.76 2.74321962193326 0.0167803780667408 18 2.79 2.77539191557036 0.0146080844296415 19 2.79 2.77645905833423 0.0135409416657670 20 2.78 2.76552860576942 0.0144713942305801 21 2.81 2.79399998913 0.0160000108699974 22 2.81 2.79312559033691 0.0168744096630915 23 2.79 2.7786970918881 0.0113029081118987 24 2.79 2.78661543382987 0.00338456617013350 25 2.79 2.77300245745318 0.0169975425468185 26 2.8 2.77625884006461 0.0237411599353856 27 2.8 2.76446232791001 0.0355376720899852 28 2.8 2.78836958253649 0.0116304174635080 29 2.77 2.88476173678217 -0.114761736782168 30 2.78 2.82413068226428 -0.0441306822642762 31 2.75 2.78372836862127 -0.0337283686212699 32 2.74 2.73996164239519 3.8357604806194e-05 33 2.74 2.75877957957929 -0.0187795795792862 34 2.72 2.73380189457873 -0.0138018945787346 35 2.71 2.69621452590184 0.0137854740981571 36 2.71 2.70350096445939 0.00649903554061337 37 2.7 2.69614615209339 0.00385384790661369 38 2.69 2.69221393788909 -0.00221393788909374 39 2.7 2.66576674804139 0.0342332519586095 40 2.71 2.68160134305123 0.0283986569487689 41 2.76 2.75189349254558 0.0081065074544231 42 2.76 2.79848867019142 -0.0384886701914184 43 2.75 2.76515380316382 -0.0151538031638188 44 2.74 2.74451081442063 -0.00451081442062851 45 2.71 2.75450691104412 -0.0445069110441221 46 2.73 2.71299626818182 0.0170037318181819 47 2.73 2.70525084415745 0.0247491558425481 48 2.73 2.71803611070996 0.0119638892900444 49 2.72 2.71371766453665 0.00628233546335499 50 2.72 2.70966979623314 0.0103302037668604 51 2.75 2.70292432620375 0.0470756737962525 52 2.82 2.72600865851773 0.0939913414822695 53 2.85 2.83617596030517 0.0138240396948315 54 2.83 2.87282404420348 -0.042824044203476 55 2.85 2.84343943734001 0.0065605626599945 56 2.85 2.84119557838112 0.0088044216188834 57 2.79 2.84854325538758 -0.0585432553875784 58 2.81 2.81561821419967 -0.00561821419966657 59 2.8 2.79434411221761 0.00565588778239379 60 2.79 2.78992499172116 7.50082788414375e-05 61 2.79 2.77557639942042 0.0144236005795833 62 2.8 2.77844406102976 0.0215559389702356 63 2.8 2.79056600835385 0.00943399164615455 64 2.86 2.80132868614762 0.0586713138523782 65 2.86 2.8627467998242 -0.00274679982420212 66 2.85 2.87082323129981 -0.0208232312998087 67 2.81 2.87163929721046 -0.0616392972104638 68 2.79 2.82228939116698 -0.0322893911669753 69 2.78 2.78068174401399 -0.00068174401399057 70 2.77 2.80414002736271 -0.0341400273627124 71 2.78 2.76626068331384 0.0137393166861632 72 2.85 2.76583332296513 0.084166677034867 73 2.82 2.8146923884354 0.00530761156460136 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 2.81330949377627 2.74994549516141 2.87667349239112 75 2.80670043609036 2.72933453982566 2.88406633235507 76 2.8255977817419 2.73640155150082 2.91479401198298 77 2.82752207414863 2.72789048742234 2.92715366087491 78 2.83210995402273 2.72303686541707 2.94118304262838 79 2.83529185265718 2.71753182445425 2.95305188086011 80 2.83791244178525 2.71206368403718 2.96376119953332 81 2.82839004296240 2.69494194289683 2.96183814302797 82 2.84230710995816 2.70166970029954 2.98294451961679 83 2.8426819226621 2.69520525813558 2.99015858718862 84 2.85371828938593 2.69970578286699 3.00773079590486 85 2.82 2.65971794314826 2.98028205685174

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/11g1a1212013612.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/11g1a1212013612.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/25mhp1212013612.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/25mhp1212013612.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/3hb2a1212013612.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t12120137137q4vz9scdzik5lz/3hb2a1212013612.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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