review workshop 9

*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, 04 Dec 2009 03:37:14 -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/04/t1259923076fp0cna71ygw5du1.htm/, Retrieved Fri, 04 Dec 2009 11:38:01 +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/04/t1259923076fp0cna71ygw5du1.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:

» Textbox « » Textfile « » CSV «

12.610 10.862 52.929 56.902 81.776 87.876 82.103 72.846 60.632 33.521 15.342 7.758 8.668 13.082 38.157 58.263 81.153 88.476 72.329 75.845 61.108 37.665 12.755 2.793 12.935 19.533 33.404 52.074 70.735 69.702 61.656 82.993 53.990 32.283 15.686 2.713 12.842 19.244 48.488 54.464 84.192 84.458 85.793 75.163 68.212 49.233 24.302 5.402 15.058 33.559 70.358 85.934 94.452 129.305 113.882 107.256 94.274 57.842 26.611 14.521

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 0.0856933077970092 beta 0.133966475305803 gamma 0.210070820415668 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.668 8.90730328460187 -0.239303284601871 14 13.082 13.4491526080878 -0.367152608087789 15 38.157 38.8689753281552 -0.711975328155155 16 58.263 58.7788482637078 -0.515848263707817 17 81.153 81.3648054271869 -0.211805427186917 18 88.476 88.927276416743 -0.451276416742985 19 72.329 79.2169136883903 -6.88791368839036 20 75.845 69.5013926970677 6.34360730293231 21 61.108 58.7010105481081 2.40698945189192 22 37.665 32.8357017859856 4.82929821401444 23 12.755 15.1771948283939 -2.42219482839394 24 2.793 7.54035851209682 -4.74735851209682 25 12.935 7.90045159257558 5.03454840742442 26 19.533 12.5956782493181 6.9373217506819 27 33.404 38.4897169640234 -5.08571696402337 28 52.074 57.9903263769801 -5.91632637698005 29 70.735 79.9827780515775 -9.24777805157747 30 69.702 86.694324305443 -16.9923243054429 31 61.656 74.7322227784386 -13.0762227784386 32 82.993 67.2368556359704 15.7561443640296 33 53.99 56.9540077741217 -2.96400777412166 34 32.283 32.2065078819177 0.076492118082264 35 15.686 13.8251062600636 1.86089373993636 36 2.713 6.34659467776843 -3.63359467776843 37 12.842 8.56782900638849 4.27417099361151 38 19.244 13.3254124000935 5.91858759990655 39 48.488 35.6819224637679 12.8060775362321 40 54.464 56.6368096885508 -2.17280968855079 41 84.192 78.7366457030856 5.45535429691436 42 84.458 85.9225951108235 -1.46459511082354 43 85.793 76.2593356966418 9.53366430335817 44 75.163 77.0882215200617 -1.92522152006171 45 68.212 61.1589032714238 7.05309672857624 46 49.233 35.8697335321788 13.3632664678212 47 24.302 16.5385274953842 7.7634725046158 48 5.402 6.85831393575046 -1.45631393575046 49 15.058 12.0794910712933 2.97850892870668 50 33.559 18.5960439127449 14.9629560872551 51 70.358 51.6702178853299 18.6877821146701 52 85.934 77.918561917365 8.01543808263507 53 94.452 114.34047554971 -19.8884755497099 54 129.305 122.43703248642 6.86796751358001 55 113.882 114.427829459730 -0.545829459730129 56 107.256 113.081087749935 -5.82508774993509 57 94.274 93.4000780841675 0.873921915832483 58 57.842 57.6310282321955 0.210971767804516 59 26.611 26.4432844991622 0.167715500837801 60 14.521 9.35159589871144 5.16940410128856 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 19.4184456467906 15.2065935006238 23.6302977929575 62 32.3219652694893 27.4778707914938 37.1660597474849 63 78.4603759484315 70.0861179514407 86.8346339454222 64 109.412722972227 97.5294342771035 121.296011667351 65 150.387317610432 133.341551005239 167.433084215626 66 170.851430593446 150.344425896385 191.358435290508 67 156.846912860106 136.833576216481 176.860249503732 68 153.451626386386 132.794137037388 174.109115735384 69 128.706729261245 110.376448001314 147.037010521176 70 79.1953544194529 66.9397997572367 91.450909081669 71 36.3126601141522 29.3546295683339 43.2706906599705 72 14.1058458897621 11.7828798339761 16.4288119455482

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/1hjes1259923032.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/1hjes1259923032.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/2frhr1259923032.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/2frhr1259923032.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/3yl1c1259923032.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259923076fp0cna71ygw5du1/3yl1c1259923032.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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