exponential smoothing 3 multiplicatief

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 07 May 2008 11:10:33 -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/07/t1210180293v984s2s4imr4aue.htm/, Retrieved Wed, 07 May 2008 19:11:37 +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

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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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0 beta 0.00350348394533219 gamma 0.323270481307047 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50556 50171.6294214468 384.3705785532 14 43901 43650.1812576848 250.818742315227 15 48572 48256.4676951532 315.532304846805 16 43899 43485.1985085089 413.801491491133 17 37532 37061.6413558757 470.358644124302 18 40357 39576.6526546217 780.347345378323 19 35489 34786.650148218 702.34985178199 20 29027 28496.6182790210 530.38172097904 21 34485 33333.4935209155 1151.50647908451 22 42598 40405.2191833129 2192.78081668707 23 30306 28538.3337504759 1767.66624952406 24 26451 24889.1034369438 1561.89656305622 25 47460 53355.5401722728 -5895.5401722728 26 50104 46378.1540860573 3725.84591394269 27 61465 51270.7390149161 10194.2609850839 28 53726 46232.6955071596 7493.3044928404 29 39477 39432.5263564694 44.4736435305895 30 43895 42191.9369247986 1703.06307520135 31 31481 37080.816722788 -5599.81672278798 32 29896 30352.2776035735 -456.277603573522 33 33842 35676.2518023742 -1834.25180237415 34 39120 43506.0448835144 -4386.04488351444 35 33702 30795.1657936726 2906.83420632741 36 25094 26857.2219833691 -1763.22198336914 37 51442 54400.0506041289 -2958.05060412890 38 45594 50298.2412433926 -4704.24124339261 39 52518 57665.7021707106 -5147.70217071064 40 48564 51405.7332016236 -2841.73320162356 41 41745 41666.5442893953 78.4557106047141 42 49585 45136.3423104853 4448.65768951467 43 32747 37236.7638680837 -4489.76386808373 44 33379 31880.7944786431 1498.2055213569 45 35645 37021.0515737432 -1376.05157374321 46 37034 44402.1753879587 -7368.17538795872 47 35681 33471.6859842105 2209.31401578949 48 20972 27719.3739188528 -6747.37391885277 49 58552 56342.3028500604 2209.69714993962 50 54955 51411.0243093201 3543.97569067989 51 65540 59011.6182069235 6528.38179307654 52 51570 53188.602251375 -1618.602251375 53 51145 43912.8987163837 7232.10128361627 54 46641 49044.5896431648 -2403.58964316481 55 35704 37674.9200302113 -1970.92003021127 56 33253 34066.5997294566 -813.599729456648 57 35193 38490.6902626285 -3297.6902626285 58 41668 44210.1382392391 -2542.1382392391 59 34865 35959.7782250809 -1094.77822508091 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 26857.6013646130 24478.2762125892 29236.9265166367 61 59991.8837560807 57612.5586040569 62371.2089081044 62 55248.8989103105 52869.5737582868 57628.2240623343 63 64239.7147668079 61860.3896147841 66619.0399188316 64 55340.2970781711 52960.9719261474 57719.6222301948 65 48590.0613135507 46210.7361615269 50969.3864655744 66 50698.5736447383 48319.2484927146 53077.8987967620 67 38895.3886427095 36516.0634906858 41274.7137947333 68 35491.9302311022 33112.6050790785 37871.2553831259 69 39286.0961869925 36906.7710349688 41665.4213390163 70 45537.5100181403 43158.1848661165 47916.835170164 71 37362.2967168488 37352.3001481867 37372.2932855109

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/1gec31210180229.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/1gec31210180229.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/28yux1210180229.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/28yux1210180229.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/335cy1210180229.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t1210180293v984s2s4imr4aue/335cy1210180229.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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