Correctie exponential smoothing Nathalie Wouters

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 11:02:29 -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/Jun/01/t1212339837k9ebhm1snjaxw2f.htm/, Retrieved Sun, 01 Jun 2008 17:04:01 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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7840 8292 8534 8441 8602 8468 8832 9006 8749 8714 8193 8251 8192 9056 9407 9068 9431 9907 10044 10838 10871 11127 11303 11349 11493 12694 13227 12253 12234 12491 13248 14042 14392 14834 15542 15518 16197 17325 24016 23671 24998 25329 25904 26548 26752 26967 27034 27056 27476 28497 29085 28720 29067 29249 29672 29761 30066 30315 30571 30757 30742 31310 31381 31470 31226 31081 31061 31114 30828 30418 30195 29877 29192 29876 29409 28458 28340 28164 28438 28053

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.959966669295933 beta 0.130110948060397 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8534 8744 -210 4 8441 8968.17754302367 -527.177543023674 5 8602 8822.02959557856 -220.029595578560 6 8468 8943.25126551266 -475.251265512663 7 8832 8760.10872303131 71.8912769686904 8 9006 9111.18416143127 -105.184161431267 9 8749 9279.13535064118 -530.135350641178 10 8714 8972.93250461495 -258.932504614952 11 8193 8894.73411878923 -701.734118789234 12 8251 8303.81282562604 -52.8128256260425 13 8192 8329.23790818928 -137.237908189281 14 9056 8256.47641242689 799.52358757311 15 9407 9182.8369634874 224.163036512600 16 9068 9584.86901316931 -516.869013169315 17 9431 9210.97693114353 220.023068856473 18 9907 9571.95804623956 335.041953760441 19 10044 10085.2009254041 -41.2009254040859 20 10838 10232.1170958797 605.882904120328 21 10871 11075.8882665190 -204.888266518972 22 11127 11115.7551471162 11.2448528838122 23 11303 11364.5071250363 -61.5071250363308 24 11349 11535.7372554282 -186.737255428176 25 11493 11563.4267455855 -70.426745585486 26 12694 11693.9739948881 1000.02600511193 27 13227 12977.0256274598 249.974372540206 28 12253 13571.2750349484 -1318.27503494835 29 12234 12495.4018650369 -261.401865036885 30 12491 12401.4420508270 89.5579491730277 31 13248 12655.5779430222 592.422056977832 32 14042 13466.4414204106 575.558579589439 33 14392 14333.0050391153 58.9949608846910 34 14834 14711.0534001296 122.946599870389 35 15542 15165.8495005589 376.150499441057 36 15518 15910.6949200358 -392.694920035789 37 16197 15868.4259139594 328.574086040635 38 17325 16559.5907307978 765.409269202162 39 24016 17765.7040447481 6250.29595525188 40 23671 25017.8013116783 -1346.80131167833 41 24998 24808.7200079244 189.279992075568 42 25329 26097.8670395035 -768.867039503471 43 25904 26371.1916921549 -467.191692154913 44 26548 26875.7613654420 -327.761365442024 45 26752 27473.2413981464 -721.241398146401 46 26967 27602.9090962116 -635.909096211599 47 27034 27735.066531716 -701.066531716024 48 27056 27717.1102673361 -661.11026733608 49 27476 27654.9365757111 -178.936575711083 50 28497 28033.2839896417 463.716010358283 51 29085 29086.4756036924 -1.47560369238272 52 28720 29692.9144673101 -972.914467310104 53 29067 29245.2852690496 -178.285269049597 54 29249 29538.2053979704 -289.205397970389 55 29672 29688.5235173937 -16.5235173936780 56 29761 30098.5433302561 -337.543330256056 57 30066 30158.2349270049 -92.2349270049199 58 30315 30441.8940717223 -126.894071722301 59 30571 30676.4322473689 -105.432247368852 60 30757 30918.4043422091 -161.404342209069 61 30742 31086.4853384461 -344.485338446073 62 31310 31035.787713021 274.212286978986 63 31381 31613.2688970065 -232.268897006503 64 31470 31675.5341356798 -205.534135679791 65 31226 31737.7921938740 -511.79219387404 66 31081 31442.1287666297 -361.128766629681 67 31061 31245.991439975 -184.991439974987 68 31114 31195.8342432055 -81.8342432054524 69 30828 31234.4832421938 -406.483242193804 70 30418 30910.7093825127 -492.709382512658 71 30195 30442.6208293491 -247.620829349089 72 29877 30178.8807384717 -301.880738471697 73 29192 29825.3473830002 -633.34738300023 74 29876 29074.5106321134 801.489367886625 75 29409 29801.1771020037 -392.177102003654 76 28458 29332.9797741262 -874.97977412615 77 28340 28292.0210976522 47.9789023477751 78 28164 28143.0646569137 20.9353430863339 79 28438 27970.7621705184 467.237829481634 80 28053 28285.2542159061 -232.254215906061 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 27899.2481559247 26227.8560670217 29570.6402448277 82 27736.1984020166 25270.1499092258 30202.2468948074 83 27573.1486481085 24384.1227674904 30762.1745287266 84 27410.0988942004 23518.2887617854 31301.9090266155 85 27247.0491402923 22653.8523032412 31840.2459773435 86 27083.9993863842 21782.0317143601 32385.9670584084 87 26920.9496324761 20898.1961062891 32943.7031586632 88 26757.8998785681 19999.7406908545 33516.0590662816 89 26594.8501246600 19085.1570683776 34104.5431809424 90 26431.8003707519 18153.5732348823 34710.0275066215 91 26268.7506168438 17204.5053838724 35332.9958498152 92 26105.7008629357 16237.7150964624 35973.686629409

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/1cl521212339743.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/1cl521212339743.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/2auop1212339743.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/2auop1212339743.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/3um1t1212339743.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212339837k9ebhm1snjaxw2f/3um1t1212339743.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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