*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: Tue, 21 Dec 2010 00:16:41 +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/Dec/21/t12928904901rmaqyx4td16uy3.htm/, Retrieved Tue, 21 Dec 2010 01:14:51 +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/Dec/21/t12928904901rmaqyx4td16uy3.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:

Dataseries X:

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101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.800425855140645 beta 0.0331010367938548 gamma 0.155499080750997 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 104.73 103.368149038462 1.36185096153842 14 104.86 104.608075407099 0.251924592900835 15 105.03 104.98042940301 0.049570596990165 16 105.62 105.610877397986 0.00912260201413062 17 105.63 105.625858141324 0.0041418586764479 18 105.63 105.60487857382 0.0251214261796378 19 105.94 106.117190518229 -0.177190518229409 20 106.61 106.116205435251 0.493794564749024 21 107.69 107.668710544731 0.0212894552693683 22 107.78 107.852324410432 -0.0723244104318752 23 107.93 107.954507754413 -0.0245077544134489 24 108.48 108.10639878838 0.373601211619913 25 108.14 108.929524867571 -0.789524867570535 26 108.48 108.417361551599 0.0626384484012732 27 108.48 108.631283288652 -0.151283288652067 28 108.89 109.093742822335 -0.203742822335499 29 108.93 108.926581581002 0.00341841899826534 30 109.21 108.894050432639 0.315949567361073 31 109.47 109.628952151016 -0.158952151016308 32 109.8 109.659953710454 0.14004628954639 33 111.73 110.901838588991 0.828161411008736 34 111.85 111.736959034911 0.113040965089311 35 112.12 112.002479362695 0.117520637305205 36 112.15 112.297653199882 -0.14765319988237 37 112.17 112.670892042672 -0.500892042671921 38 112.67 112.427285156356 0.242714843643924 39 112.8 112.794558607827 0.00544139217296902 40 113.44 113.400841701517 0.0391582984831871 41 113.53 113.460974484271 0.0690255157290238 42 114.53 113.518834901439 1.01116509856136 43 114.51 114.842065865226 -0.332065865225957 44 115.05 114.785793761209 0.264206238791175 45 116.67 116.193715801099 0.476284198900672 46 117.07 116.760970550048 0.309029449952277 47 116.92 117.224675529598 -0.304675529598185 48 117 117.203668665873 -0.20366866587301 49 117.02 117.549610208994 -0.52961020899393 50 117.35 117.333833669063 0.016166330937466 51 117.36 117.53414631254 -0.174146312539676 52 117.82 118.014708885544 -0.194708885544003 53 117.88 117.89935868561 -0.0193586856101575 54 118.24 117.924153820167 0.31584617983269 55 118.5 118.639167571678 -0.139167571678371 56 118.8 118.750930857801 0.0490691421989595 57 119.76 119.982663244492 -0.222663244491997 58 120.09 119.956183411041 0.133816588958965 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 59 120.226867301325 119.495761998643 120.957972604006 60 120.427206857907 119.478515540984 121.375898174829 61 120.905792757828 119.770313880513 122.041271635144 62 121.124637143078 119.819586722415 122.429687563741 63 121.299445237922 119.835785915359 122.763104560485 64 121.91671637142 120.301944326895 123.531488415945 65 121.965772222373 120.205238931287 123.726305513459 66 122.020092346141 120.117721406749 123.922463285533 67 122.463432799368 120.422145862008 124.504719736729 68 122.691377167944 120.513364446082 124.869389889805 69 123.873046525867 121.559947566095 126.186145485638 70 124.039400422033 121.592429857695 126.486370986372

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/173hn1292890597.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/173hn1292890597.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/2hdzq1292890597.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/2hdzq1292890597.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/3hdzq1292890597.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928904901rmaqyx4td16uy3/3hdzq1292890597.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = no ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = no ;

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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