*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 17:06:15 +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/t1291829676ibzqyvznorfwrrf.htm/, Retrieved Wed, 08 Dec 2010 18:34:37 +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/t1291829676ibzqyvznorfwrrf.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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.594091053904783 beta 0.374196561823787 gamma 0.693700862612219 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 5 200779 193857.86875 6921.13124999998 6 204428 202551.478155215 1876.52184478543 7 207617 210393.918864677 -2776.91886467711 8 212071 206924.464049405 5146.53595059502 9 214239 224646.345835572 -10407.3458355723 10 215883 220255.125632632 -4372.12563263174 11 223484 220316.192412998 3167.80758700179 12 221529 221172.28584846 356.714151539549 13 225247 229166.872676244 -3919.87267624363 14 226699 229269.353236709 -2570.35323670949 15 231406 231864.630352412 -458.630352412263 16 232324 228309.265272053 4014.73472794739 17 237192 236620.575448753 571.424551246804 18 236727 240117.463158815 -3390.46315881546 19 240698 242983.992694058 -2285.99269405808 20 240688 239360.235012365 1327.76498763464 21 245283 244265.9632392 1017.03676079967 22 243556 246171.349805591 -2615.34980559099 23 247826 249241.026895512 -1415.0268955116 24 245798 246777.547048244 -979.547048243956 25 250479 249337.381124557 1141.61887544286 26 249216 249434.025038334 -218.025038333988 27 251896 253938.908589686 -2042.90858968601 28 247616 250758.440679939 -3142.44067993888 29 249994 251683.178258106 -1689.17825810626 30 246552 248138.500344917 -1586.50034491657 31 248771 249435.591086078 -664.59108607826 32 247551 245189.82881535 2361.17118465033 33 249745 249442.377324503 302.622675496677 34 245742 247201.669079551 -1459.66907955092 35 249019 248953.641809106 65.3581908937776 36 245841 246275.742891004 -434.742891004193 37 248771 247948.28297532 822.717024679645 38 244723 245296.617566287 -573.617566287227 39 246878 247977.661584934 -1099.66158493413 40 246014 244181.084601035 1832.91539896512 41 248496 247773.278821491 722.721178508742 42 244351 244865.181820142 -514.181820142257 43 248016 247642.779986517 373.220013483427 44 246509 246083.780703617 425.21929638306 45 249426 248750.925691315 675.074308685347 46 247840 245679.501734709 2160.49826529145 47 251035 251103.843136672 -68.8431366720179 48 250161 250006.452020969 154.547979031107 49 254278 253232.567542782 1045.43245721792 50 250801 251531.187881904 -730.187881904189 51 253985 254699.595714861 -714.595714860945 52 249174 253227.049688093 -4053.04968809334 53 251287 253214.524668936 -1927.52466893601 54 247947 247596.251904122 350.748095877643 55 249992 250000.816227863 -8.8162278632517 56 243805 246754.018924213 -2949.01892421348 57 255812 246987.817578133 8824.18242186715 58 250417 249780.655217727 636.344782272761 59 253033 253699.236931496 -666.23693149563 60 248705 250533.415141752 -1828.41514175225 61 253950 256296.606901658 -2346.60690165771 62 251484 249212.671099804 2271.32890019621 63 251093 253164.489084398 -2071.48908439768 64 245996 247952.863976388 -1956.86397638821 65 252721 252581.568103102 139.431896898343 66 248019 247915.279431006 103.720568993769 67 250464 248515.016731504 1948.98326849574 68 245571 245776.496867017 -205.496867017326 69 252690 252477.589619012 212.410380987654 70 250183 248302.468241621 1880.53175837855 71 253639 251330.245378833 2308.75462116735 72 254436 249131.649158065 5304.35084193503 73 265280 261381.487880857 3898.51211914272 74 268705 262843.121427061 5861.87857293943 75 270643 272219.00667257 -1576.00667256973 76 271480 271554.64455014 -74.644550140365 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 282015.865498848 276525.680709346 287506.050288351 78 282650.455993896 275563.000601895 289737.911385897 79 286082.545418822 276985.700226495 295179.390611149 80 286760.633392828 275328.962373197 298192.304412459

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/14ryc1291827971.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/14ryc1291827971.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/24ryc1291827971.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/24ryc1291827971.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/3figf1291827971.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291829676ibzqyvznorfwrrf/3figf1291827971.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 4 ; par2 = Triple ; 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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