exponential smoothing model tafelbier Maarten Verhaegen

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 07:11:49 -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/Jun/01/t12123260607ihpumv9n7hrpvj.htm/, Retrieved Sun, 01 Jun 2008 13:14:20 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0,63 0,64 0,65 0,65 0,65 0,65 0,65 0,66 0,65 0,66 0,66 0,66 0,66 0,68 0,69 0,7 0,71 0,71 0,7 0,7 0,7 0,7 0,71 0,7 0,7 0,7 0,69 0,7 0,69 0,69 0,69 0,7 0,7 0,71 0,71 0,71 0,72 0,73 0,74 0,74 0,74 0,74 0,75 0,75 0,76 0,76 0,76 0,76 0,76 0,77 0,77 0,78 0,78 0,78 0,78 0,78 0,78 0,78 0,8 0,8 0,8 0,81 0,81 0,81 0,8 0,81 0,81 0,81 0,8 0,82 0,83 0,83

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.692780535122199 beta 0.000961035668292444 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.66 0.642931344526887 0.0170686554731130 14 0.68 0.672968781756433 0.0070312182435669 15 0.69 0.686151407991656 0.00384859200834398 16 0.7 0.697125959947919 0.00287404005208125 17 0.71 0.707415363872179 0.00258463612782078 18 0.71 0.707527165499493 0.00247283450050673 19 0.7 0.698022406242879 0.00197759375712137 20 0.7 0.699000495635157 0.000999504364843085 21 0.7 0.700963021739085 -0.00096302173908469 22 0.7 0.702396296022734 -0.00239629602273406 23 0.71 0.713723183028984 -0.00372318302898378 24 0.7 0.704902961986993 -0.00490296198699336 25 0.7 0.691375147695947 0.00862485230405297 26 0.7 0.713212493024162 -0.0132124930241621 27 0.69 0.711571455565236 -0.0215714555652361 28 0.7 0.704671632031416 -0.00467163203141574 29 0.69 0.709631505095134 -0.0196315050951338 30 0.69 0.69435415404041 -0.00435415404041006 31 0.69 0.680278989707719 0.00972101029228079 32 0.7 0.686336117477076 0.0136638825229239 33 0.7 0.696449614308298 0.00355038569170241 34 0.71 0.700543270147116 0.00945672985288382 35 0.71 0.719758398003111 -0.00975839800311118 36 0.71 0.706329419034816 0.0036705809651838 37 0.72 0.702756933184547 0.0172430668154527 38 0.73 0.723940593365488 0.00605940663451188 39 0.74 0.733052390659313 0.0069476093406865 40 0.74 0.751888581219213 -0.011888581219213 41 0.74 0.74723752220306 -0.00723752220305962 42 0.74 0.745328199187258 -0.00532819918725769 43 0.75 0.734236190649055 0.0157638093509449 44 0.75 0.745534422587639 0.0044655774123612 45 0.76 0.745871666830757 0.0141283331692433 46 0.76 0.75921714565002 0.000782854349980378 47 0.76 0.766839818961247 -0.00683981896124686 48 0.76 0.759240285978673 0.000759714021327018 49 0.76 0.757468066346126 0.00253193365387361 50 0.77 0.765228649803522 0.00477135019647845 51 0.77 0.773881751186837 -0.00388175118683709 52 0.78 0.779649682156555 0.000350317843445302 53 0.78 0.785059912331307 -0.00505991233130698 54 0.78 0.785340211931307 -0.00534021193130729 55 0.78 0.780489099574688 -0.000489099574688234 56 0.78 0.776845728438716 0.00315427156128445 57 0.78 0.77911468660341 0.000885313396589704 58 0.78 0.779111167591526 0.000888832408474038 59 0.8 0.784514624186743 0.0154853758132567 60 0.8 0.79460340426113 0.00539659573887052 61 0.8 0.796404250362448 0.00359574963755216 62 0.81 0.805830971936683 0.00416902806331698 63 0.81 0.811445674255775 -0.00144567425577458 64 0.81 0.820616388807891 -0.0106163888078910 65 0.8 0.816825298821848 -0.0168252988218480 66 0.81 0.808910455846066 0.00108954415393403 67 0.81 0.80993961915437 6.03808456306476e-05 68 0.81 0.807632048764273 0.00236795123572742 69 0.8 0.80856017343223 -0.00856017343223037 70 0.82 0.801932141347813 0.0180678586521871 71 0.83 0.823978585316508 0.00602141468349215 72 0.83 0.824199614852678 0.00580038514732162 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.825563640825694 0.80863116389052 0.842496117760868 74 0.832830199915946 0.812183186668991 0.8534772131629 75 0.833796897778278 0.810055292429213 0.857538503127342 76 0.84127297780816 0.814676011798923 0.867869943817398 77 0.842838584316136 0.813764296722004 0.871912871910267 78 0.852480652525385 0.820910105174526 0.884051199876244 79 0.852340631195274 0.818704769723606 0.885976492666942 80 0.850517633520536 0.81499685148956 0.886038415551513 81 0.846132586677521 0.808924206899066 0.883340966455977 82 0.853854619152912 0.814601304627878 0.893107933677945 83 0.859833579011665 0.818679831590243 0.900987326433087 84 0.855589151959457 -7.08416398191686 8.79534228583578

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/1zx9l1212325904.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/1zx9l1212325904.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/2fpqb1212325904.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/2fpqb1212325904.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/3ifmh1212325904.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123260607ihpumv9n7hrpvj/3ifmh1212325904.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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