*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: Wed, 08 Dec 2010 17:06:08 +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/08/t1291829014j5sgph55xmzbiup.htm/, Retrieved Wed, 08 Dec 2010 18:23:34 +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/08/t1291829014j5sgph55xmzbiup.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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186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.415713187131023 beta 0.533706293812228 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 194207 194612 -405 4 190855 198435.779317733 -7580.77931773296 5 200779 197594.554556400 3184.44544360027 6 204428 201935.104602940 2492.89539705965 7 207617 206541.263747221 1075.73625277937 8 212071 210796.963398662 1274.03660133804 9 214239 215417.768021061 -1178.76802106085 10 215883 218757.377635710 -2874.37763570971 11 223484 220754.365416378 2729.6345836221 12 221529 225686.635575184 -4157.63557518445 13 225247 226833.327320933 -1586.32732093311 14 226699 228696.989365262 -1997.98936526186 15 231406 229946.226677341 1459.77332265853 16 232324 232956.779610955 -632.779610955215 17 237192 234957.036677536 2234.96332246382 18 236727 238645.320804960 -1918.32080495975 19 240698 240181.414522373 516.585477627203 20 240688 242844.345062178 -2156.34506217801 21 245283 243917.677556878 1365.32244312158 22 243556 246757.936050369 -3201.93605036903 23 247826 246989.115427959 836.88457204125 24 245798 249084.964327941 -3286.96432794144 25 250479 248737.200210162 1741.79978983794 26 249216 250866.410583469 -1650.41058346943 27 251896 251219.259847184 676.740152816288 28 247616 252689.683848399 -5073.68384839906 29 249994 250643.888895825 -649.888895825279 30 246552 250292.933808889 -3740.93380888866 31 248771 247826.994302543 944.005697456509 32 247551 247518.091288691 32.9087113087589 33 249745 246837.734657400 2907.26534260032 34 245742 247997.317293432 -2255.31729343228 35 249019 246510.361831912 2508.63816808816 36 245841 247560.433879139 -1719.43387913931 37 248771 246471.351984364 2299.64801563646 38 244723 247563.275451180 -2840.27545117974 39 246878 245888.296603914 989.703396086057 40 246014 246025.0747197 -11.0747197000892 41 248496 245743.359041207 2752.64095879253 42 244351 247221.281409036 -2870.28140903582 43 248016 245724.855066068 2291.14493393217 44 246509 246882.43516799 -373.435167990014 45 249426 246849.460591542 2576.53940845776 46 247840 248614.482911658 -774.482911657542 47 251035 248814.607511768 2220.39248823244 48 250161 250752.377002849 -591.377002848982 49 254278 251390.048764230 2887.95123576961 50 250801 254114.86927131 -3313.86927131008 51 253985 253526.267195070 458.732804929517 52 249174 254607.764023163 -5433.76402316292 53 251287 252034.089813545 -747.089813544939 54 247947 251242.971997772 -3295.97199777234 55 249992 248660.977076874 1331.02292312571 56 243805 248297.797346093 -4492.79734609343 57 255812 244516.767423929 11295.2325760708 58 250417 249805.088808503 611.911191497289 59 253033 250787.976578887 2245.02342111259 60 248705 252947.871166762 -4242.87116676228 61 253950 251469.301919353 2480.69808064739 62 251484 253336.19844105 -1852.19844105004 63 251093 252990.907797722 -1897.90779772206 64 245996 252205.528751997 -6209.52875199678 65 252721 248250.051670194 4470.94832980601 66 248019 249726.553448325 -1707.5534483254 67 250464 248255.717821012 2208.28217898804 68 245571 248902.695496927 -3331.69549692675 69 252690 246507.432299951 6182.5677000492 70 250183 249439.092312525 743.907687474944 71 253639 250274.879502114 3364.12049788595 72 254436 252946.316900932 1489.68309906818 73 265280 255169.040073343 10110.9599266574 74 268705 263219.047696420 5485.95230357972 75 270643 270563.540009396 79.4599906041985 76 271480 275678.11186009 -4198.11186008976 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 278083.010876332 271587.184362263 284578.837390401 78 282233.120353865 274529.303656385 289936.937051344 79 286383.229831398 276869.191679495 295897.267983300 80 290533.339308930 278707.334571495 302359.344046366

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/1pjle1291827964.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/1pjle1291827964.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/20akz1291827964.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/20akz1291827964.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/30akz1291827964.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829014j5sgph55xmzbiup/30akz1291827964.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 4 ; par2 = Double ; par3 = additive ;

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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