*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 17:30:18 +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/May/31/t1275327126eeeug6elr9gkltz.htm/, Retrieved Mon, 31 May 2010 19:32:07 +0200

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/May/31/t1275327126eeeug6elr9gkltz.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

66857.2 64722.8 68489.6 71342.9 63542.5 69425.0 58927.9 61009.0 66837.0 66147.6 65982.3 65527.5 65914.6 59189.9 66211.4 66400.8 60167.7 64547.9 57706.2 58642.6 60082.1 63414.8 66044.0 57628.5 62838.8 55758.6 61004.5 66173.4 57489.0 59552.2 57061.8 55895.3 56314.7 61232.8 60014.1 57685.4 60403.1 52349.7 55693.3 65676.1 54898.8 55518.2 53779.1 52340.9 55704.4 60330.3 52837.4 55388.1 60383.4 52070.3 54077.0 62887.8 49212.8 57722.0 53936.8 46991.0 54984.2 56485.1 51277.8 53596.4 54252.5 49413.0 53213.2 58695.3 48723.5 54510.0 49454.1 46136.6 54622.5 50583.0 53224.3 53056.4

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 0.0775686079515321 beta 0.141640000501599 gamma 0.670983617686526 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 65914.6 67882.8211538462 -1968.22115384619 14 59189.9 60840.47026691 -1650.57026690995 15 66211.4 67781.3746025152 -1569.97460251523 16 66400.8 67894.4482735782 -1493.64827357818 17 60167.7 61290.5070304832 -1122.80703048316 18 64547.9 65531.5536835978 -983.65368359779 19 57706.2 56242.4995444508 1463.70045554917 20 58642.6 58333.6105024026 308.989497597358 21 60082.1 64141.0969500315 -4058.99695003153 22 63414.8 63023.1526432903 391.647356709655 23 66044 62824.5332446759 3219.46675532407 24 57628.5 62588.4272212497 -4959.92722124972 25 62838.8 61197.347055258 1641.45294474201 26 55758.6 54534.7579067309 1223.8420932691 27 61004.5 61683.2493009422 -678.749300942232 28 66173.4 61857.2262541424 4316.17374585757 29 57489 55941.8344356091 1547.1655643909 30 59552.2 60513.8112049269 -961.611204926929 31 57061.8 52779.1624848204 4282.63751517962 32 55895.3 54443.1521958585 1452.14780414152 33 56314.7 57717.2762321708 -1402.5762321708 34 61232.8 59670.707936096 1562.092063904 35 60014.1 61436.6335907519 -1422.5335907519 36 57685.4 55850.444039921 1834.95596007899 37 60403.1 59219.4360586351 1183.66394136492 38 52349.7 52405.0010665963 -55.3010665962938 39 55693.3 58404.7731654094 -2711.47316540936 40 65676.1 61618.3658799707 4057.73412002931 41 54898.8 54071.9998767351 826.800123264853 42 55518.2 57130.3236761668 -1612.12367616685 43 53779.1 52678.9226391937 1100.17736080632 44 52340.9 52397.046114724 -56.1461147239534 45 55704.4 53823.5958047275 1880.80419527246 46 60330.3 57939.0440372382 2391.25596276176 47 52837.4 58003.4916354791 -5166.09163547907 48 55388.1 54183.4665800441 1204.63341995594 49 60383.4 57133.9001922602 3249.49980773985 50 52070.3 49769.0088337006 2301.29116629938 51 54077 54389.6085942253 -312.608594225334 52 62887.8 62087.3738016488 800.426198351226 53 49212.8 52361.200446708 -3148.40044670802 54 57722 53630.5600598703 4091.43994012966 55 53936.8 51391.9074259386 2544.89257406144 56 46991 50613.866840064 -3622.86684006401 57 54984.2 53030.8750428926 1953.32495710743 58 56485.1 57536.9576520233 -1051.85765202333 59 51277.8 52688.0535885619 -1410.25358856188 60 53596.4 53174.9447240306 421.455275969405 61 54252.5 57394.173539077 -3141.67353907702 62 49413 48940.3314044521 472.668595547941 63 53213.2 51774.8435729036 1438.35642709644 64 58695.3 60290.1576265646 -1594.85762656457 65 48723.5 47900.6277648954 822.872235104638 66 54510 53969.1802079779 540.819792022077 67 49454.1 50469.0328443371 -1014.93284433713 68 46136.6 45529.4362067718 607.163793228196 69 54622.5 51704.3695499936 2918.13045000644 70 50583 54414.3738982551 -3831.37389825513 71 53224.3 49086.6041996828 4137.69580031715 72 53056.4 51157.0694026702 1899.33059732983 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 53321.3382965011 48761.1131486803 57881.5634443219 74 47418.5094364662 42840.4384200492 51996.5804528833 75 50879.1338343962 46278.613075513 55479.6545932794 76 57454.7843500648 52826.7345494586 62082.8341506711 77 46752.1828967761 42091.076178765 51413.2896147872 78 52640.0896489957 47939.9806730561 57340.1986249353 79 48186.8937696138 43441.4547912524 52932.3327479752 80 44392.963503145 39595.5228870434 49190.4041192467 81 52007.4353384743 47151.0188631171 56863.8518138315 82 50337.8038692353 45415.1780311231 55260.4297073476 83 50305.9031508743 45309.6195882438 55302.1867135048 84 50690.8750551609 45613.315172303 55768.4349380187

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/1zbrb1275327014.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/1zbrb1275327014.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/2rk8e1275327014.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/2rk8e1275327014.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/3rk8e1275327014.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275327126eeeug6elr9gkltz/3rk8e1275327014.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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