Aankoop nieuwe en tweedehandswagens

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 11:37:01 -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/t12123418472clq5t3yml7vs9y.htm/, Retrieved Sun, 01 Jun 2008 17:37:31 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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102.8 103.1 103.1 103.3 103.5 103.3 103.5 103.8 103.9 103.9 104.2 104.6 104.9 105.2 105.2 105.6 105.6 106.2 106.3 106.4 106.9 107.2 107.3 107.3 107.4 107.55 107.87 108.37 108.38 107.92 108.03 108.14 108.3 108.64 108.66 109.04 109.03 109.03 109.54 109.75 109.83 109.65 109.82 109.95 110.12 110.15 110.2 109.99 110.14 110.14 110.81 110.97 110.99 109.73 109.81 110.02 110.18 110.21 110.25 110.36 110.51 110.64 110.95 111.18 111.19 111.69 111.7 111.83 111.77 111.73 112.01 111.86 112.04

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 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 103.1 102.8 0.299999999999997 3 103.1 103.1 0 4 103.3 103.1 0.200000000000003 5 103.5 103.3 0.200000000000003 6 103.3 103.5 -0.200000000000003 7 103.5 103.3 0.200000000000003 8 103.8 103.5 0.299999999999997 9 103.9 103.8 0.100000000000009 10 103.9 103.9 0 11 104.2 103.9 0.299999999999997 12 104.6 104.2 0.399999999999991 13 104.9 104.6 0.300000000000011 14 105.2 104.9 0.299999999999997 15 105.2 105.2 0 16 105.6 105.2 0.399999999999991 17 105.6 105.6 0 18 106.2 105.6 0.600000000000009 19 106.3 106.2 0.0999999999999943 20 106.4 106.3 0.100000000000009 21 106.9 106.4 0.5 22 107.2 106.9 0.299999999999997 23 107.3 107.2 0.0999999999999943 24 107.3 107.3 0 25 107.4 107.3 0.100000000000009 26 107.55 107.4 0.149999999999991 27 107.87 107.55 0.320000000000007 28 108.37 107.87 0.5 29 108.38 108.37 0.0099999999999909 30 107.92 108.38 -0.459999999999994 31 108.03 107.92 0.109999999999999 32 108.14 108.03 0.109999999999999 33 108.3 108.14 0.159999999999997 34 108.64 108.3 0.340000000000003 35 108.66 108.64 0.019999999999996 36 109.04 108.66 0.38000000000001 37 109.03 109.04 -0.0100000000000051 38 109.03 109.03 0 39 109.54 109.03 0.510000000000005 40 109.75 109.54 0.209999999999994 41 109.83 109.75 0.0799999999999983 42 109.65 109.83 -0.179999999999993 43 109.82 109.65 0.169999999999987 44 109.95 109.82 0.130000000000010 45 110.12 109.95 0.170000000000002 46 110.15 110.12 0.0300000000000011 47 110.2 110.15 0.0499999999999972 48 109.99 110.2 -0.210000000000008 49 110.14 109.99 0.150000000000006 50 110.14 110.14 0 51 110.81 110.14 0.670000000000002 52 110.97 110.81 0.159999999999997 53 110.99 110.97 0.019999999999996 54 109.73 110.99 -1.25999999999999 55 109.81 109.73 0.0799999999999983 56 110.02 109.81 0.209999999999994 57 110.18 110.02 0.160000000000011 58 110.21 110.18 0.0299999999999869 59 110.25 110.21 0.0400000000000063 60 110.36 110.25 0.109999999999999 61 110.51 110.36 0.150000000000006 62 110.64 110.51 0.129999999999995 63 110.95 110.64 0.310000000000002 64 111.18 110.95 0.230000000000004 65 111.19 111.18 0.0099999999999909 66 111.69 111.19 0.5 67 111.7 111.69 0.0100000000000051 68 111.83 111.7 0.129999999999995 69 111.77 111.83 -0.0600000000000023 70 111.73 111.77 -0.039999999999992 71 112.01 111.73 0.280000000000001 72 111.86 112.01 -0.150000000000006 73 112.04 111.86 0.180000000000007 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 112.04 111.539710105102 112.540289894898 75 112.04 111.332483245517 112.747516754483 76 112.04 111.173472483523 112.906527516477 77 112.04 111.039420210204 113.040579789796 78 112.04 110.921317786552 113.158682213448 79 112.04 110.814545034029 113.265454965971 80 112.04 110.716357354661 113.363642645339 81 112.04 110.624966491034 113.455033508966 82 112.04 110.539130315306 113.540869684694 83 112.04 110.457944441756 113.622055558244 84 112.04 110.380726132217 113.699273867783 85 112.04 110.306944967047 113.773055032953

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/1hn3u1212341815.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/1hn3u1212341815.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/227lv1212341815.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/227lv1212341815.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/3x4331212341815.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123418472clq5t3yml7vs9y/3x4331212341815.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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