*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 09:18:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb.htm/, Retrieved Wed, 20 Jan 2010 17:19:08 +0100

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/Jan/20/t1264004344wv5t925aazpiqkb.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 «

103,6 103,7 103,8 104 104 104,1 104,2 104,3 104,4 104,5 104,7 104,7 104,9 105 105,2 105,3 105,4 105,5 105,7 105,8 105,9 106 106,1 106,2 106,6 106,8 107 107,1 107,3 107,4 107,6 107,7 107,9 108,2 108,3 108,5 108,92 109,23 109,41 109,65 109,91 110,01 110,2 110,49 110,57 110,72 110,94 111,09 111,28 111,41 111,62 111,76 111,89 112,04 112,12 112,3 112,47 112,59 112,78 112,73 112,99 113,1 113,33 113,38 113,68 113,65 113,81 113,88 114,02 114,25 114,28 114,38 114,73 114,97 115,05 115,29 115,37 115,54 115,76 115,92 116,02 116,21 116,26 116,51

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.72568966705914 beta 0.184950675591331 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 103.8 103.8 -1.4210854715202e-14 4 104 103.9 0.09999999999998 5 104 104.085990646125 -0.085990646125154 6 104.1 104.125468413334 -0.0254684133341812 7 104.2 104.205448250716 -0.00544825071608557 8 104.3 104.299225266498 0.000774733502282743 9 104.4 104.397622219872 0.00237778012808576 10 104.5 104.497501625644 0.00249837435563904 11 104.7 104.597803869198 0.102196130801644 12 104.7 104.784172181489 -0.0841721814892509 13 104.9 104.823997614924 0.0760023850762792 14 105 104.990260872716 0.00973912728359494 15 105.2 105.109744723465 0.0902552765345206 16 105.3 105.299772085633 0.000227914367258109 17 105.4 105.424498111258 -0.0244981112583389 18 105.5 105.527992657623 -0.0279926576231446 19 105.7 105.625194163033 0.0748058369671298 20 105.8 105.807035673381 -0.00703567338057098 21 105.9 105.928541339806 -0.0285413398062957 22 106 106.030609839193 -0.0306098391929055 23 106.1 106.127068895461 -0.0270688954611416 24 106.2 106.222464477636 -0.022464477636035 25 106.6 106.318186328078 0.28181367192208 26 106.8 106.672543815171 0.127456184829086 27 107 106.931992429375 0.0680075706249568 28 107.1 107.157427556640 -0.0574275566403486 29 107.3 107.284127965612 0.0158720343876126 30 107.4 107.466151423966 -0.0661514239658914 31 107.6 107.579772674080 0.0202273259201178 32 107.7 107.758792937280 -0.0587929372796907 33 107.9 107.872578012424 0.0274219875757069 34 108.2 108.052608858946 0.14739114105447 35 108.3 108.339482446957 -0.0394824469567965 36 108.5 108.485444595645 0.0145554043553915 37 108.92 108.672575034371 0.247424965629492 38 109.23 109.061905093176 0.168094906824464 39 109.41 109.416227307533 -0.00622730753259759 40 109.65 109.643209882938 0.00679011706162669 41 109.91 109.880550416608 0.029449583391866 42 110.01 110.138287319528 -0.128287319527942 43 110.2 110.264337869122 -0.0643378691223973 44 110.49 110.428160651551 0.0618393484485011 45 110.57 110.691848816094 -0.121848816093760 46 110.72 110.805882220194 -0.0858822201944065 47 110.94 110.934489375026 0.00551062497409305 48 111.09 111.130158991657 -0.0401589916573357 49 111.28 111.287296628283 -0.00729662828256039 50 111.41 111.467302812387 -0.0573028123874906 51 111.62 111.603329025622 0.0166709743784281 52 111.76 111.795274776282 -0.0352747762820513 53 111.89 111.944789565052 -0.0547895650521752 54 112.04 112.072788993480 -0.0327889934804801 55 112.12 112.212353175778 -0.0923531757780154 56 112.3 112.296296899269 0.00370310073097357 57 112.47 112.450444688387 0.0195553116125495 58 112.59 112.618720914377 -0.0287209143767484 59 112.78 112.748108752947 0.0318912470529256 60 112.73 112.925762551707 -0.195762551707276 61 112.99 112.911935718927 0.0780642810725851 62 113.1 113.107299726806 -0.00729972680589697 63 113.33 113.239736210298 0.0902637897021634 64 113.38 113.455088446087 -0.0750884460871077 65 113.68 113.540368142424 0.139631857575708 66 113.65 113.800209084728 -0.150209084728303 67 113.81 113.829554868301 -0.0195548683008155 68 113.88 113.951090474958 -0.0710904749582966 69 114.02 114.025685688732 -0.00568568873229935 70 114.25 114.146981365132 0.103018634867709 71 114.28 114.360989476847 -0.0809894768474777 72 114.38 114.43059465529 -0.0505946552901122 73 114.73 114.515466389233 0.214533610767276 74 114.97 114.821532979782 0.148467020217836 75 115.05 115.099582495729 -0.0495824957289557 76 115.29 115.227254720762 0.0627452792376886 77 115.37 115.444863521643 -0.0748635216426834 78 115.54 115.552563095751 -0.0125630957509486 79 115.76 115.703787266745 0.056212733254597 80 115.92 115.912466039043 0.00753396095716141 81 116.02 116.086830313366 -0.0668303133661396 82 116.21 116.198259451800 0.0117405482001942 83 116.26 116.368282431346 -0.108282431345572 84 116.51 116.436672654023 0.0733273459772192 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 116.646696976844 116.480435032221 116.812958921466 86 116.803508402376 116.584229184955 117.022787619797 87 116.960319827909 116.685724740546 117.234914915271 88 117.117131253441 116.784571144477 117.449691362405 89 117.273942678973 116.880673561429 117.667211796517 90 117.430754104506 116.974035907327 117.887472301685 91 117.587565530038 117.064703314969 118.110427745108 92 117.744376955571 117.152737975142 118.336015935999 93 117.901188381103 117.238208136533 118.564168625674 94 118.057999806636 117.321182874186 118.794816739085 95 118.214811232168 117.401729578008 119.027892886328 96 118.371622657700 117.479912789376 119.263332526024

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/1ilch1264004307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/1ilch1264004307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/25ngu1264004307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/25ngu1264004307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/3ifmr1264004307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264004344wv5t925aazpiqkb/3ifmr1264004307.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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