Exponential smoothing

*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: Tue, 21 Dec 2010 18:33:15 +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/21/t12929562625hikfqly6l1blr3.htm/, Retrieved Tue, 21 Dec 2010 19:31:03 +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/21/t12929562625hikfqly6l1blr3.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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1038.00 934.00 988.00 870.00 854.00 834.00 872.00 954.00 870.00 1238.00 1082.00 1053.00 934.00 787.00 1081.00 908.00 995.00 825.00 822.00 856.00 887.00 1094.00 990.00 936.00 1097.00 918.00 926.00 907.00 899.00 971.00 1087.00 1000.00 1071.00 1190.00 1116.00 1070.00 1314.00 1068.00 1185.00 1215.00 1145.00 1251.00 1363.00 1368.00 1535.00 1853.00 1866.00 2023.00 1373.00 1968.00 1424.00 1160.00 1243.00 1375.00 1539.00 1773.00 1906.00 2076.00 2004.00

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 0.389032955231208 beta 0.0286225511594326 gamma 0.689233804798979 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 934 918.07264957265 15.9273504273501 14 787 782.112350583715 4.8876494162846 15 1081 1080.12000196049 0.87999803951493 16 908 911.495010425234 -3.49501042523389 17 995 1005.67074573912 -10.6707457391155 18 825 838.811063549857 -13.811063549857 19 822 848.742573118919 -26.7425731189189 20 856 928.928850993235 -72.9288509932346 21 887 816.126740170604 70.8732598293964 22 1094 1204.34923810212 -110.349238102125 23 990 994.841460579284 -4.8414605792841 24 936 955.284108655832 -19.2841086558321 25 1097 834.55868680411 262.44131319589 26 918 790.708583897266 127.291416102734 27 926 1136.8676451593 -210.867645159301 28 907 883.885624774277 23.1143752257228 29 899 985.54998548892 -86.5499854889204 30 971 787.16186261572 183.83813738428 31 1087 870.05429339561 216.94570660439 32 1000 1029.8221541756 -29.8221541755963 33 1071 999.052725606927 71.9472743930733 34 1190 1316.10018296636 -126.100182966362 35 1116 1149.43838524672 -33.4383852467192 36 1070 1096.90005240976 -26.9000524097585 37 1314 1095.98725803912 218.012741960885 38 1068 981.587901416325 86.4120985836752 39 1185 1172.63630507475 12.3636949252548 40 1215 1110.70520145293 104.294798547072 41 1145 1204.3527485473 -59.352748547295 42 1251 1137.28919222821 113.710807771793 43 1363 1212.9442126035 150.055787396498 44 1368 1248.13399220433 119.866007795674 45 1535 1325.47804151983 209.521958480171 46 1853 1621.20571160027 231.794288399727 47 1866 1645.33839843436 220.661601565638 48 2023 1709.77799076074 313.222009239262 49 1373 1963.47512299638 -590.475122996381 50 1968 1489.28648777257 478.713512227433 51 1424 1816.29573481096 -392.295734810956 52 1160 1645.66934082907 -485.669340829074 53 1243 1444.33868958243 -201.338689582428 54 1375 1396.78294379575 -21.7829437957541 55 1539 1435.39063657518 103.609363424823 56 1773 1439.64051733905 333.35948266095 57 1906 1640.01406344116 265.985936558845 58 2076 1969.93512922857 106.064870771429 59 2004 1941.9151411507 62.0848588492952 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 1983.32266925458 1596.32674222829 2370.31859628088 61 1730.81467477465 1313.98314478306 2147.64620476623 62 1939.34438933134 1493.15557342406 2385.53320523862 63 1710.7761800172 1235.58064989665 2185.97171013775 64 1655.25358981908 1151.30452415144 2159.20265548673 65 1769.8110747687 1237.28576510002 2302.33638443738 66 1885.65077858288 1324.66631803821 2446.63523912755 67 1995.23519670278 1405.86020693255 2584.61018647301 68 2064.47134570337 1446.73492505565 2682.2077663511 69 2111.62027558709 1465.51894867981 2757.72160249437 70 2272.5937897027 1598.09698804128 2947.09059136412 71 2185.48244835068 1482.53689069361 2888.42800600775

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/1g9g31292956391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/1g9g31292956391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/2rjfo1292956391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/2rjfo1292956391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/3rjfo1292956391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929562625hikfqly6l1blr3/3rjfo1292956391.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 12 ; 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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