Exponential Smoothing

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Dec 2009 10:28:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18.htm/, Retrieved Thu, 03 Dec 2009 18:30:00 +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/2009/Dec/03/t12598613961qnyew3brlmwc18.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

Uitleg in Word document

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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96.96 93.11 95.62 98.30 96.38 100.82 99.06 94.03 102.07 99.31 98.64 101.82 99.14 97.63 100.06 101.32 101.49 105.43 105.09 99.48 108.53 104.34 106.10 107.35 103.00 104.50 105.17 104.84 106.18 108.86 107.77 102.74 112.63 106.26 108.86 111.38 106.85 107.86 107.94 111.38 111.29 113.72 111.88 109.87 113.72 111.71 114.81 112.05 111.54 110.87 110.87 115.48 111.63 116.24 113.56 106.01 110.45 107.77 108.61 108.19

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 0.176261864801442 beta 1 gamma 0.600923944155917 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 99.14 96.9701078086023 2.16989219139769 14 97.63 96.2030591186773 1.42694088132269 15 100.06 99.431378904446 0.628621095554024 16 101.32 101.501848185809 -0.181848185808690 17 101.49 102.267284361111 -0.777284361111484 18 105.43 106.577629786737 -1.14762978673657 19 105.09 105.527295103797 -0.437295103797226 20 99.48 100.520382405752 -1.04038240575231 21 108.53 109.072585741727 -0.542585741727265 22 104.34 106.155697584904 -1.81569758490407 23 106.1 104.900162390693 1.19983760930700 24 107.35 108.418033329171 -1.0680333291713 25 103 106.238976848037 -3.23897684803737 26 104.5 102.78944014273 1.71055985726996 27 105.17 104.605862470763 0.564137529236874 28 104.84 105.107030858014 -0.267030858013840 29 106.18 104.356347770034 1.82365222996579 30 108.86 108.286005211030 0.573994788969728 31 107.77 107.418581716426 0.351418283574333 32 102.74 101.840546586726 0.899453413274145 33 112.63 111.226187332072 1.40381266792828 34 106.26 108.310144341984 -2.05014434198399 35 108.86 108.864245321722 -0.00424532172155523 36 111.38 111.237255696141 0.142744303859160 37 106.85 108.419593267117 -1.56959326711744 38 107.86 108.334309597288 -0.474309597288027 39 107.94 109.479637970686 -1.53963797068599 40 111.38 109.065373453684 2.31462654631638 41 111.29 110.141518075464 1.14848192453621 42 113.72 113.662120131314 0.0578798686858164 43 111.88 112.640248565069 -0.760248565068508 44 109.87 106.798333089354 3.0716669106464 45 113.72 117.568547610295 -3.8485476102947 46 111.71 111.207156295411 0.502843704588955 47 114.81 113.161886492191 1.64811350780889 48 112.05 116.154619004939 -4.10461900493868 49 111.54 111.030774728233 0.509225271766581 50 110.87 111.681541542628 -0.81154154262758 51 110.87 112.005327353228 -1.13532735322833 52 115.48 113.439640460457 2.04035953954320 53 111.63 113.646580715151 -2.01658071515121 54 116.24 115.306057199403 0.93394280059708 55 113.56 113.356329030139 0.203670969861363 56 106.01 109.066993650808 -3.05699365080753 57 110.45 113.672010559872 -3.22201055987207 58 107.77 108.156438072855 -0.38643807285456 59 108.61 108.787487038676 -0.177487038676162 60 108.19 106.65977398156 1.53022601844008 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 103.951517191193 101.767746706038 106.135287676349 62 102.799120961628 100.333140101633 105.265101821623 63 102.145077353275 99.1337009786908 105.156453727859 64 104.307857934344 100.438799593681 108.176916275008 65 101.251979512091 96.4615776124803 106.042381411702 66 103.587240815721 97.5004115900556 109.674070041386 67 100.445910954070 93.2043623606451 107.687459547494 68 94.270080290677 86.0728884430293 102.467272138325 69 98.2534086164423 88.1760156747464 108.330801558138 70 95.1546421609472 83.7527780355253 106.556506286369 71 95.949063648979 82.6914742122405 109.206653085718 72 94.9583946571643 79.9845144089064 109.932274905422

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/16way1259861292.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/16way1259861292.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/2pidj1259861292.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/2pidj1259861292.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/3dwd91259861292.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t12598613961qnyew3brlmwc18/3dwd91259861292.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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')

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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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