WS9

*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: Fri, 11 Dec 2009 05:54:10 -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/11/t1260536095mudrt4t5ev04ag7.htm/, Retrieved Fri, 11 Dec 2009 13:54:59 +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/11/t1260536095mudrt4t5ev04ag7.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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7.55 7.55 7.59 7.59 7.59 7.57 7.57 7.59 7.6 7.64 7.64 7.76 7.76 7.76 7.77 7.83 7.94 7.94 7.94 8.09 8.18 8.26 8.28 8.28 8.28 8.29 8.3 8.3 8.31 8.33 8.33 8.34 8.48 8.59 8.67 8.67 8.67 8.71 8.72 8.72 8.72 8.74 8.74 8.74 8.74 8.79 8.85 8.86 8.87 8.92 8.96 8.97 8.99 8.98 8.98 9.01 9.01 9.03 9.05 9.05

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.848800087938736 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7.76 7.61197688096642 0.148023119033584 14 7.76 7.73508127617569 0.0249187238243094 15 7.77 7.75493610895619 0.0150638910438081 16 7.83 7.81142301245571 0.0185769875442885 17 7.94 7.91825231476319 0.0217476852368153 18 7.94 7.92207334921433 0.0179266507856743 19 7.94 7.96741586091488 -0.0274158609148749 20 8.09 7.98028943044056 0.109710569559438 21 8.18 8.10026553869293 0.0797344613070692 22 8.26 8.2256801643389 0.0343198356610923 23 8.28 8.26180499176366 0.0181950082363436 24 8.28 8.40836139135682 -0.128361391356817 25 8.28 8.32404003197007 -0.0440400319700682 26 8.29 8.26178724169145 0.0282127583085447 27 8.3 8.28049566383511 0.0195043361648874 28 8.3 8.34201160340643 -0.0420116034064311 29 8.31 8.40140676092787 -0.0914067609278693 30 8.33 8.30624710113261 0.0237528988673894 31 8.33 8.34917362973838 -0.0191736297383756 32 8.34 8.39073301192205 -0.0507330119220519 33 8.48 8.36953476099503 0.11046523900497 34 8.59 8.51474895400571 0.075251045994289 35 8.67 8.58206011379746 0.0879398862025411 36 8.67 8.76881379003755 -0.0988137900375463 37 8.67 8.72246943279367 -0.0524694327936661 38 8.71 8.66169196419698 0.0483080358030215 39 8.72 8.69414710354374 0.0258528964562625 40 8.72 8.75183648926944 -0.0318364892694394 41 8.72 8.81502799922603 -0.0950279992260281 42 8.74 8.73248099782015 0.00751900217984769 43 8.74 8.75429194053674 -0.0142919405367401 44 8.74 8.79615133617384 -0.0561513361738371 45 8.74 8.79515626383475 -0.0551562638347498 46 8.79 8.79477670626116 -0.00477670626116122 47 8.85 8.79530500654702 0.0546949934529781 48 8.86 8.92645100310957 -0.0664510031095702 49 8.87 8.91479209814778 -0.0447920981477825 50 8.92 8.8749092980496 0.0450907019504001 51 8.96 8.90017101411346 0.0598289858865417 52 8.97 8.97779367639901 -0.00779367639900919 53 8.99 9.05305911344782 -0.0630591134478191 54 8.98 9.01251553925291 -0.0325155392529144 55 8.98 8.99644891115725 -0.0164489111572497 56 9.01 9.03049561520607 -0.0204956152060696 57 9.01 9.06028623396056 -0.0502862339605645 58 9.03 9.07230834976358 -0.0423083497635783 59 9.05 9.04936918378332 0.000630816216675711 60 9.05 9.11698370075069 -0.0669837007506882 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 9.10844210717998 8.99246245371989 9.22442176064008 62 9.11955162961144 8.96758237073146 9.2715208884914 63 9.10772760470569 8.92718827756804 9.28826693184334 64 9.12406608020662 8.91869333327727 9.32943882713597 65 9.19822045377927 8.9697205010155 9.42672040654304 66 9.21543730970699 8.9669768471807 9.46389777223328 67 9.22888640735084 8.9621029751272 9.49566983957449 68 9.27666433366325 8.99192855770998 9.5614001096165 69 9.31958340399799 9.01804824319786 9.6211185647981 70 9.376237243929 9.05835748267164 9.69411700518637 71 9.39516424409414 9.06284389133888 9.7274845968494 72 9.45284213993226 5.96526564771901 12.9404186321455

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/13ef41260536048.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/13ef41260536048.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/2ymlk1260536048.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/2ymlk1260536048.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/39pn71260536048.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260536095mudrt4t5ev04ag7/39pn71260536048.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')

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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