triple model, additief

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 29 Apr 2008 07:08:05 -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/Apr/29/t1209474526aw25d9oix73an6w.htm/, Retrieved Tue, 29 Apr 2008 15:08:51 +0200

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Dataseries X:

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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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0512572023235812 beta 0.000425534174427011 gamma 0.368605978860725 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50556 50513.9134722223 42.0865277777484 14 43901 43931.2207583048 -30.2207583047712 15 48572 48571.4461160293 0.553883970744209 16 43899 43787.7905745671 111.209425432899 17 37532 37307.3093522476 224.690647752446 18 40357 39878.9830941167 478.016905883254 19 35489 35015.15205761 473.847942389999 20 29027 28634.6593337897 392.340666210319 21 34485 33503.7889993035 981.211000696465 22 42598 40907.1239125659 1690.87608743407 23 30306 28398.0378202951 1907.96217970492 24 26451 24599.1622363261 1851.83776367391 25 47460 53185.4184385885 -5725.41843858849 26 50104 46281.8642188605 3822.13578113946 27 61465 51130.4482996314 10334.5517003686 28 53726 46915.5430119018 6810.45698809817 29 39477 40818.6392113434 -1341.63921134340 30 43895 43399.0913610316 495.908638968445 31 31481 38535.1926514119 -7054.1926514119 32 29896 31740.6385184782 -1844.63851847820 33 33842 36701.3022621234 -2859.30226212342 34 39120 44156.1382214790 -5036.13822147904 35 33702 31378.1915624761 2323.80843752393 36 25094 27581.0424649262 -2487.04246492615 37 51442 53294.9844857177 -1852.98448571766 38 45594 49928.8458265101 -4334.84582651011 39 52518 56636.6482653951 -4118.64826539515 40 48564 50448.0286568089 -1884.02865680889 41 41745 41053.9275843764 691.072415623552 42 49585 44380.5739934001 5204.42600659989 43 32747 37117.1504914156 -4370.15049141558 44 33379 32281.5692064946 1097.43079350543 45 35645 37037.8103717865 -1392.81037178655 46 37034 43806.1958880855 -6772.19588808546 47 35681 33512.7370643893 2168.26293561075 48 20972 28024.8078272207 -7052.80782722075 49 58552 53725.9660216681 4826.03397833186 50 54955 49833.8901653443 5121.10983465568 51 65540 57101.8439860219 8438.15601397814 52 51570 52338.4574206093 -768.457420609338 53 51145 43902.2386717266 7242.7613282734 54 46641 49143.3811748015 -2502.3811748015 55 35704 38136.7130716886 -2432.71307168862 56 33253 35312.6935494417 -2059.69354944170 57 35193 39036.3464977491 -3843.34649774914 58 41668 43797.9388594381 -2129.93885943813 59 34865 36869.170106545 -2004.17010654498 60 21210 27942.7138847439 -6732.71388474385 61 56126 57814.5247119143 -1688.52471191430 62 49231 53691.6491642265 -4460.6491642265 63 59723 61628.1982867343 -1905.19828673426 64 48103 53114.4667700878 -5011.46677008781 65 47472 47261.784274631 210.215725368987 66 50497 48733.7084571041 1763.29154289586 67 40059 37969.3898106767 2089.61018932334 68 34149 35507.0592861316 -1358.05928613158 69 36860 38642.3638867991 -1782.36388679905 70 46356 44108.2942354146 2247.7057645854 71 36577 37447.4877720121 -870.487772012071 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 26925.1294928216 19538.9820340103 34311.2769516328 73 58905.8204086582 51509.9682503327 66301.6725669837 74 53899.849991913 46494.2976103394 61305.4023734865 75 62958.6113331107 55543.3631834882 70373.8594827331 76 53456.1756117601 46031.2361283391 60881.1150951812 77 49686.5034737539 42251.8770699529 57121.129877555 78 51690.8278320165 44246.5189005386 59135.1367634944 79 40950.252547475 33496.2654604233 48404.2396345266 80 37175.0836819099 29711.4227909023 44638.7445729175 81 40231.6052411939 32758.2748774764 47704.9356049115 82 47198.2894120937 39715.2938866533 54681.2849375341 83 39331.7823201656 31839.1259238426 46824.4387164886

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/1s4jk1209474483.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/1s4jk1209474483.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/2uxjf1209474483.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/2uxjf1209474483.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/32ixl1209474483.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t1209474526aw25d9oix73an6w/32ixl1209474483.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=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')

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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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