*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 21 Jan 2010 04:12:44 -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/21/t1264073808b80cu7nw6nlgkt4.htm/, Retrieved Thu, 21 Jan 2010 12:36:52 +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/21/t1264073808b80cu7nw6nlgkt4.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:

» Textbox « » Textfile « » CSV «

104.0 99.0 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145.0 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179.0 190.6 190.0 181.6 174.8 180.5 196.8 193.8 197.0 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244.0 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191.0 159.7 163.4 157.6 166.2 176.7 198.3 226.2 216.2 235.9

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 0.936888096626754 beta 0.828413409801924 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 105.4 94 11.4 4 107.1 108.528413856660 -1.42841385666023 5 110.7 109.929403679192 0.770596320807812 6 117.1 113.988703394520 3.11129660547955 7 118.7 122.655750040687 -3.95575004068711 8 126.5 121.631585905084 4.86841409491615 9 127.5 132.653201568736 -5.15320156873645 10 134.6 130.286127059423 4.31387294057691 11 131.8 140.136771032064 -8.33677103206435 12 135.9 131.664753625936 4.23524637406433 13 142.7 138.258414253318 4.44158574668188 14 141.7 148.492642671913 -6.79264267191309 15 153.4 142.929677951704 10.4703220482955 16 145 161.666517380681 -16.6665173806808 17 137.7 142.043779788519 -4.34377978851876 18 148.3 130.594727678295 17.7052723217053 19 152.2 153.544774772892 -1.34477477289232 20 169.4 157.603338568676 11.7966614313244 21 168.6 183.129708171458 -14.5297081714576 22 161.1 172.714263433619 -11.6142634336185 23 174.1 156.016078191186 18.0839218088142 24 179 181.177255412026 -2.17725541202628 25 190.6 185.666142185149 4.93385781485097 26 190 200.646664629951 -10.6466646299511 27 181.6 192.766778181890 -11.1667781818905 28 174.8 175.732724587261 -0.93272458726065 29 180.5 167.562917833625 12.9370821663748 30 196.8 182.428434085557 14.3715659144427 31 193.8 209.792114063494 -15.9921140634945 32 197 196.296453613774 0.703546386225923 33 216.3 198.988802627721 17.3111973722788 34 221.4 230.676413252619 -9.27641325261911 35 217.9 230.254699199796 -12.3546991997960 36 229.7 217.360114807289 12.3398851927106 37 227.4 237.17895585589 -9.77895585589027 38 204.2 228.685170525644 -24.4851705256441 39 196.6 187.409616097757 9.19038390224287 40 198.8 184.817226509449 13.9827734905508 41 207.5 197.567228936841 9.93277106315867 42 190.7 214.231960486689 -23.5319604866891 43 201.6 181.280107302819 20.3198926971814 44 210.5 205.183425167594 5.31657483240585 45 223.5 219.156669863080 4.34333013692046 46 223.8 235.589084885880 -11.7890848858802 47 231.2 227.757362038525 3.44263796147504 48 244 236.867995900552 7.13200409944841 49 234.7 254.970520049637 -20.270520049637 50 250.2 231.667373345923 18.5326266540773 51 265.7 259.102172707726 6.59782729227436 52 287.6 280.476176680754 7.12382331924613 53 283.3 307.871997784259 -24.5719977842586 54 295.4 286.501300458197 8.8986995418034 55 312.3 303.395454615529 8.9045453844713 56 333.8 327.206176383825 6.59382361617509 57 347.7 353.969679125931 -6.26967912593091 58 383.2 363.815429052923 19.3845709470772 59 407.1 412.741300397082 -5.64130039708209 60 413.6 433.842344555343 -20.2423445553430 61 362.7 425.553139948472 -62.8531399484724 62 321.9 328.560139187149 -6.66013918714884 63 239.4 279.044553711655 -39.6445537116554 64 191 167.856909148111 23.1430908518893 65 159.7 133.456323831866 26.2436761681338 66 163.4 122.329161767816 41.0708382321836 67 157.6 156.969728244327 0.630271755672595 68 166.2 154.211182603582 11.9888173964179 69 176.7 171.399211959866 5.3007880401336 70 198.3 186.435410356935 11.8645896430654 71 226.2 216.829628167094 9.370371832906 72 216.2 252.159675901215 -35.9596759012148 73 235.9 217.111134404971 18.7888655950291 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 247.938464450437 215.801375336682 280.075553564193 75 261.162729970801 197.417509287621 324.907950653982 76 274.386995491165 172.100652888896 376.673338093434 77 287.611261011529 141.070531905368 434.15199011769 78 300.835526531893 105.022386029901 496.648667033884 79 314.059792052257 64.4349482905303 563.684635813983 80 327.284057572620 19.6677709464701 634.90034419877 81 340.508323092984 -28.9949950765487 710.011641262517 82 353.732588613348 -81.3209647179877 788.786141944684 83 366.956854133712 -137.115284357096 871.02899262452 84 380.181119654076 -196.211408376065 956.573647684216 85 393.405385174440 -258.464797903691 1045.27556825257

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/18k0w1264072362.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/18k0w1264072362.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/286yx1264072362.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/286yx1264072362.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/3rof41264072362.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/21/t1264073808b80cu7nw6nlgkt4/3rof41264072362.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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