opl oef 3

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 08 May 2008 08:39:49 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/08/t1210257631z2t1717n867r0s6.htm/, Retrieved Thu, 08 May 2008 16:40:36 +0200

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.587763292801995 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 53152 56421 -3269 3 53536 54499.6017958303 -963.601795830276 4 52408 53933.2320313632 -1525.23203136316 5 41454 53036.7566303221 -11582.7566303221 6 38271 46228.8374535598 -7957.83745355983 7 35306 41551.5127082725 -6245.51270827245 8 26414 37880.6295936215 -11466.6295936215 9 31917 31140.9656263337 776.034373666269 10 38030 31597.0901451274 6432.90985487265 11 27534 35378.1184237257 -7844.1184237257 12 18387 30767.6335498679 -12380.6335498679 13 50556 23490.7516076227 27065.2483923773 14 43901 39398.7111232303 4502.28887676971 15 48572 42044.9912585862 6527.00874141375 16 43899 45881.327408587 -1982.327408587 17 37532 44716.1881235043 -7184.18812350426 18 40357 40493.5860559244 -136.586055924403 19 35489 40413.3057859434 -4924.30578594343 20 29027 37518.9796024334 -8491.9796024334 21 34485 32527.7057088998 1957.29429110023 22 42598 33678.1314464194 8919.86855358061 23 30306 38920.9027588329 -8614.9027588329 24 26451 33857.3791461323 -7406.37914613228 25 47460 29504.1813514615 17955.8186485385 26 50104 40057.952445282 10046.0475547180 27 61465 45962.6504356885 15502.3495643115 28 53726 55074.3624617758 -1348.36246177580 29 39477 54281.8445013519 -14804.8445013519 30 43895 45580.1003478158 -1685.10034781577 31 31481 44589.6602186818 -13108.6602186818 32 29896 36884.8709243269 -6988.87092432685 33 33842 32777.0691368764 1064.93086312362 34 39120 33402.9964075924 5717.00359240761 35 33702 36763.2412640267 -3061.24126402673 36 25094 34963.9560186210 -9869.95601862104 37 51442 29162.7581693055 22279.2418306945 38 45594 42257.6787088464 3336.32129115356 39 52518 44218.6458967803 8299.35410321974 40 48564 49096.7015926184 -532.701592618447 41 41745 48783.5991504602 -7038.59915046016 42 49585 44646.5689370724 4938.43106292763 43 32747 47549.1974398944 -14802.1974398944 44 33379 38849.0091319168 -5470.00913191679 45 35645 35633.9385528844 11.0614471156077 46 37034 35640.4400654642 1393.55993453578 47 35681 36459.5234413039 -778.5234413039 48 20972 36001.9359399196 -15029.9359399196 49 58552 27167.8913012694 31384.1086987306 50 54955 45614.3183716910 9340.68162830895 51 65540 51104.428162561 14435.5718374390 52 51570 59589.1273992139 -8019.12739921391 53 51145 54875.7786736532 -3730.77867365324 54 46641 52682.9639157114 -6041.96391571136 55 35704 49131.719309622 -13427.719309622 56 33253 41239.3987933776 -7986.39879337764 57 35193 36545.2867409521 -1352.28674095211 58 41668 35750.4622332776 5917.53776672238 59 34865 39228.5737163265 -4363.57371632653 60 21210 36663.8252604342 -15453.8252604342 61 56126 27580.6340389747 28545.3659610253 62 49231 44358.5523304649 4872.44766953506 63 59723 47222.3982167163 12500.6017832837 64 48103 54569.7930828656 -6466.79308286561 65 47472 50768.8494866113 -3296.84948661135 66 50497 48831.0823764881 1665.91762351191 67 40059 49810.2476044203 -9751.24760442032 68 34149 44078.8222035187 -9929.82220351866 69 36860 38242.4372082402 -1382.43720824017 70 46356 37429.8913626329 8926.10863736707 71 36577 42676.3303672401 -6099.33036724014 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 39091.3678667039 18712.1183588240 59470.6173745837 73 39091.3678667039 15452.6182817955 62730.1174516122 74 39091.3678667039 12591.0442201596 65591.6915132481 75 39091.3678667039 10009.6927979398 68173.042935468 76 39091.3678667039 7639.49198880492 70543.2437446028 77 39091.3678667039 5435.80119977124 72746.9345336365 78 39091.3678667039 3367.79247025269 74814.943263155 79 39091.3678667039 1413.11803288704 76769.6177005207 80 39091.3678667039 -445.03538363117 78627.771117039 81 39091.3678667039 -2219.69425237858 80402.4299857863 82 39091.3678667039 -3921.1945405775 82103.9302739852 83 39091.3678667039 -5557.90084258026 83740.636575988

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/1q3qh1210257587.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/1q3qh1210257587.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/2m2ft1210257587.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/2m2ft1210257587.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/3erpv1210257587.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/3erpv1210257587.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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