smoothing- zakje friet- Keshia Vleminx

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 20:33:21 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9.htm/, Retrieved Mon, 31 May 2010 22:34:26 +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/2010/May/31/t1275338065olnvbx87ride6j9.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

2.06 2.06 2.05 2.04 2.04 2.03 2.03 2.03 2.02 2.02 2.02 2.02 2.01 2.01 2.01 2 2 1.99 1.99 1.99 1.98 1.97 1.97 1.96 1.96 1.96 1.96 1.95 1.94 1.94 1.93 1.93 1.93 1.92 1.92 1.9 1.9 1.9 1.9 1.89 1.88 1.88 1.87 1.86 1.86 1.85 1.83 1.82 1.8 1.8 1.79 1.78 1.78 1.78 1.77 1.77 1.76 1.75 1.75 1.75 1.75 1.75 1.74 1.74 1.74 1.74 1.73 1.73 1.73 1.73 1.73 1.72 1.71 1.71 1.71 1.7 1.7 1.7 1.7 1.7 1.69 1.68 1.67 1.65 1.61

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.927762771241466 beta 0.198109645413317 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2.01 2.03072115384615 -0.0207211538461549 14 2.01 2.00748144002278 0.00251855997722172 15 2.01 2.00626557568381 0.0037344243161872 16 2 1.99728079421496 0.00271920578504181 17 2 1.99827058408908 0.0017294159109249 18 1.99 1.98907661492225 0.000923385077747696 19 1.99 1.98430455738235 0.00569544261764721 20 1.99 1.98958998575807 0.000410014241930323 21 1.98 1.97963048389671 0.000369516103292167 22 1.97 1.97928465930258 -0.00928465930257993 23 1.97 1.96827554137208 0.00172445862792125 24 1.96 1.96779722654822 -0.00779722654821624 25 1.96 1.94555508744653 0.0144449125534722 26 1.96 1.95977894513417 0.000221054865829018 27 1.96 1.95925612495126 0.000743875048742071 28 1.95 1.94961058059993 0.000389419400073532 29 1.94 1.95012626385646 -0.0101262638564608 30 1.94 1.92945463390813 0.0105453660918706 31 1.93 1.93530254343693 -0.00530254343692627 32 1.93 1.92932956005059 0.000670439949406409 33 1.93 1.91898352686913 0.0110164731308733 34 1.92 1.92914984006377 -0.00914984006376707 35 1.92 1.92041752849116 -0.000417528491158947 36 1.9 1.9182269009656 -0.0182269009656035 37 1.9 1.886961010909 0.0130389890910043 38 1.9 1.89764040830256 0.0023595916974426 39 1.9 1.89831986567758 0.00168013432242087 40 1.89 1.88886988183789 0.00113011816211439 41 1.88 1.88880181242994 -0.00880181242994271 42 1.88 1.87058433140664 0.0094156685933584 43 1.87 1.87376381453316 -0.00376381453316266 44 1.86 1.86945716870631 -0.0094571687063083 45 1.86 1.84840833457007 0.0115916654299335 46 1.85 1.85570309936632 -0.00570309936631874 47 1.83 1.84948441830759 -0.0194844183075893 48 1.82 1.82349834477349 -0.00349834477348709 49 1.8 1.80604331658941 -0.00604331658940715 50 1.8 1.79262780162109 0.0073721983789079 51 1.79 1.79321038811514 -0.00321038811513552 52 1.78 1.77358625742501 0.00641374257498684 53 1.78 1.77307663592639 0.0069233640736075 54 1.78 1.7690285894445 0.010971410555505 55 1.77 1.77124954700737 -0.0012495470073739 56 1.77 1.76787655639738 0.00212344360261807 57 1.76 1.76023307832219 -0.00023307832219488 58 1.75 1.75427537268716 -0.00427537268715872 59 1.75 1.74761558586639 0.00238441413360846 60 1.75 1.74632268158529 0.0036773184147143 61 1.75 1.73990929381816 0.0100907061818423 62 1.75 1.7499650063908 3.49936092007841e-05 63 1.74 1.74916096388099 -0.00916096388099419 64 1.74 1.72980263579681 0.0101973642031861 65 1.74 1.73862686090827 0.00137313909172843 66 1.74 1.73448854722002 0.00551145277997622 67 1.73 1.73452422292915 -0.00452422292915178 68 1.73 1.73151795586241 -0.00151795586240877 69 1.73 1.72281780008888 0.00718219991111613 70 1.73 1.72730253406541 0.00269746593458664 71 1.73 1.73272939559088 -0.0027293955908827 72 1.72 1.73098199671585 -0.0109819967158451 73 1.71 1.7129336754931 -0.00293367549309709 74 1.71 1.70928773771625 0.000712262283754761 75 1.71 1.7076805134186 0.00231948658139758 76 1.7 1.70171456836556 -0.00171456836556105 77 1.7 1.69800336649949 0.00199663350050594 78 1.7 1.69401050368088 0.0059894963191156 79 1.7 1.69312066044991 0.00687933955008502 80 1.7 1.70236323854667 -0.0023632385466672 81 1.69 1.69480385424044 -0.00480385424044405 82 1.68 1.68693790496287 -0.00693790496287483 83 1.67 1.68035593379931 -0.0103559337993102 84 1.65 1.66685755060263 -0.0168575506026325 85 1.61 1.63878035710017 -0.0287803571001695 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 1.60150847439988 1.5853706468716 1.61764630192816 87 1.58931589977176 1.5651869115552 1.61344488798833 88 1.57043965239783 1.53851477396908 1.60236453082659 89 1.55843542562462 1.51857323180532 1.59829761944393 90 1.54235979062877 1.49430572087092 1.59041386038661 91 1.5243577302526 1.46781225401399 1.58090320649121 92 1.51366617570973 1.44831189557359 1.57902045584587 93 1.49567329384589 1.42118730579965 1.57015928189212 94 1.4805432472163 1.39660322112547 1.56448327330714 95 1.46985949877724 1.37614677672424 1.56357222083023 96 1.45711111608624 1.35331228687163 1.56090994530085 97 1.43852266618254 1.32433032124163 1.55271501112344

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/10bda1275337996.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/10bda1275337996.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/2b2cd1275337996.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/2b2cd1275337996.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/3b2cd1275337996.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275338065olnvbx87ride6j9/3b2cd1275337996.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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