exponential smoothing - eigen gegevensreeks - Manuella Loeckx

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 29 May 2008 01:40:25 -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/29/t1212046872m4w6iivsmx51h1h.htm/, Retrieved Thu, 29 May 2008 09:41:12 +0200

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Dataseries X:

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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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.915663434874416 beta 0.0895749531284736 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 127000 122743.575185982 4256.42481401785 14 123000 122649.613222873 350.386777127162 15 118000 118107.388716282 -107.388716281886 16 114000 114202.936887386 -202.936887385615 17 108000 108286.068362664 -286.068362664213 18 111000 111276.631612865 -276.631612864556 19 151000 151294.410955505 -294.410955504864 20 159000 159226.353052911 -226.353052910941 21 158000 158247.427387692 -247.427387692267 22 148000 148396.198542146 -396.198542146216 23 138000 138435.605664984 -435.605664984119 24 137000 137443.212949773 -443.212949772977 25 136000 136214.983508189 -214.983508188685 26 133000 131103.911634427 1896.08836557309 27 126000 127383.546322454 -1383.54632245353 28 120000 121794.435581792 -1794.43558179250 29 114000 113762.822080683 237.177919317110 30 116000 117108.97693637 -1108.97693637008 31 153000 157719.061136631 -4719.06113663127 32 162000 160876.159633024 1123.84036697622 33 161000 160375.456220262 624.543779738044 34 149000 150504.786421154 -1504.78642115393 35 139000 138797.695582466 202.30441753412 36 135000 137788.952174263 -2788.95217426325 37 130000 133680.536134512 -3680.53613451167 38 127000 124788.766097373 2211.23390262721 39 122000 120447.860552226 1552.13944777426 40 117000 117007.055305401 -7.05530540106702 41 112000 110458.534438677 1541.46556132342 42 113000 114443.871764589 -1443.87176458853 43 149000 152852.159291432 -3852.15929143186 44 157000 156584.804447601 415.195552398538 45 157000 154876.548468663 2123.45153133676 46 147000 146060.756456847 939.24354315328 47 137000 136674.123001984 325.876998015825 48 132000 135352.391311146 -3352.39131114594 49 125000 130440.551709414 -5440.55170941388 50 123000 120229.056935324 2770.94306467635 51 117000 116248.370142196 751.629857803942 52 114000 111795.411305188 2204.5886948119 53 111000 107410.782584991 3589.21741500919 54 112000 112994.544436019 -994.544436019103 55 144000 151335.221122636 -7335.22112263629 56 150000 151760.217062282 -1760.21706228246 57 149000 147857.409947338 1142.59005266248 58 134000 138135.357544721 -4135.35754472140 59 123000 124120.483048653 -1120.48304865336 60 116000 120436.755365459 -4436.75536545919 61 117000 113555.244422032 3444.75557796756 62 111000 112162.540261358 -1162.54026135805 63 105000 104463.020482013 536.979517986649 64 102000 99867.1409692748 2132.8590307252 65 95000 95657.6330475273 -657.63304752727 66 93000 95827.7625903503 -2827.76259035029 67 124000 124070.902896474 -70.9028964744939 68 130000 129641.767681409 358.23231859073 69 124000 127442.631976233 -3442.63197623273 70 115000 113876.144536925 1123.85546307501 71 106000 105738.401137215 261.59886278458 72 105000 102934.82125949 2065.17874051002 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 102903.307571317 98427.8639280625 107378.751214571 74 98323.5542514954 92110.0763425352 104537.032160456 75 92432.2995878847 84839.7688869762 100024.830288793 76 87891.7400800932 79011.0912832522 96772.3888769343 77 82053.850609248 72133.4549373877 91974.2462811082 78 82276.551366543 70733.2283516878 93819.8743813983 79 109676.905135360 92590.3460088345 126763.464261886 80 114611.560680366 94897.2659024947 134325.855458238 81 111984.005201739 90827.0292913772 133140.981112101 82 103085.615340781 81748.228907131 124423.001774431 83 94865.7846165817 73406.1867709022 116325.382462261 84 92316.458413619 70038.1589683718 114594.757858866

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/1p8tg1212046819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/1p8tg1212046819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/2w5hd1212046819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/2w5hd1212046819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/32p241212046819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212046872m4w6iivsmx51h1h/32p241212046819.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')

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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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