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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 05:39:54 -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/28/t1211974899jq508k1b7ut1n1n.htm/, Retrieved Wed, 28 May 2008 13:41:42 +0200

User-defined keywords:

Dataseries X:

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3.27 3.27 3.27 3.27 3.27 3.28 3.32 3.34 3.34 3.35 3.35 3.35 3.35 3.35 3.4 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.43 3.47 3.51 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.58 3.6 3.61 3.61 3.61 3.63 3.68 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.78 3.79 3.79 3.8 3.8 3.8 3.8 3.81 3.95 3.99 4 4.06 4.16 4.19 4.2 4.2 4.2 4.2 4.2 4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68

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 3.27 3.27 0 3 3.27 3.27 0 4 3.27 3.27 0 5 3.27 3.27 0 6 3.28 3.27 0.00999999999999979 7 3.32 3.28 0.04 8 3.34 3.32 0.02 9 3.34 3.34 0 10 3.35 3.34 0.0100000000000002 11 3.35 3.35 0 12 3.35 3.35 0 13 3.35 3.35 0 14 3.35 3.35 0 15 3.4 3.35 0.0499999999999998 16 3.42 3.4 0.02 17 3.42 3.42 0 18 3.42 3.42 0 19 3.42 3.42 0 20 3.42 3.42 0 21 3.42 3.42 0 22 3.42 3.42 0 23 3.42 3.42 0 24 3.42 3.42 0 25 3.42 3.42 0 26 3.42 3.42 0 27 3.43 3.42 0.0100000000000002 28 3.47 3.43 0.04 29 3.51 3.47 0.0399999999999996 30 3.52 3.51 0.0100000000000002 31 3.52 3.52 0 32 3.52 3.52 0 33 3.52 3.52 0 34 3.52 3.52 0 35 3.52 3.52 0 36 3.52 3.52 0 37 3.52 3.52 0 38 3.52 3.52 0 39 3.58 3.52 0.06 40 3.6 3.58 0.02 41 3.61 3.6 0.00999999999999979 42 3.61 3.61 0 43 3.61 3.61 0 44 3.63 3.61 0.02 45 3.68 3.63 0.0500000000000003 46 3.69 3.68 0.00999999999999979 47 3.69 3.69 0 48 3.69 3.69 0 49 3.69 3.69 0 50 3.69 3.69 0 51 3.69 3.69 0 52 3.69 3.69 0 53 3.69 3.69 0 54 3.78 3.69 0.0899999999999999 55 3.79 3.78 0.0100000000000002 56 3.79 3.79 0 57 3.8 3.79 0.00999999999999979 58 3.8 3.8 0 59 3.8 3.8 0 60 3.8 3.8 0 61 3.81 3.8 0.0100000000000002 62 3.95 3.81 0.14 63 3.99 3.95 0.04 64 4 3.99 0.00999999999999979 65 4.06 4 0.0599999999999996 66 4.16 4.06 0.100000000000001 67 4.19 4.16 0.0300000000000002 68 4.2 4.19 0.00999999999999979 69 4.2 4.2 0 70 4.2 4.2 0 71 4.2 4.2 0 72 4.2 4.2 0 73 4.23 4.2 0.0300000000000002 74 4.38 4.23 0.149999999999999 75 4.43 4.38 0.0499999999999998 76 4.44 4.43 0.0100000000000007 77 4.44 4.44 0 78 4.44 4.44 0 79 4.44 4.44 0 80 4.44 4.44 0 81 4.45 4.44 0.00999999999999979 82 4.45 4.45 0 83 4.45 4.45 0 84 4.45 4.45 0 85 4.45 4.45 0 86 4.45 4.45 0 87 4.45 4.45 0 88 4.45 4.45 0 89 4.46 4.45 0.00999999999999979 90 4.46 4.46 0 91 4.46 4.46 0 92 4.48 4.46 0.0200000000000005 93 4.58 4.48 0.0999999999999996 94 4.67 4.58 0.0899999999999999 95 4.68 4.67 0.00999999999999979 96 4.68 4.68 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 4.68 4.62148930680457 4.73851069319543 98 4.68 4.59725338413917 4.76274661586083 99 4.68 4.57865650659944 4.78134349340056 100 4.68 4.56297861360914 4.79702138639086 101 4.68 4.54916611260439 4.81083388739561 102 4.68 4.53667865717466 4.82332134282534 103 4.68 4.52519525676689 4.8348047432331 104 4.68 4.51450676827835 4.84549323172165 105 4.68 4.50446792041371 4.85553207958629 106 4.68 4.49497294202713 4.86502705797287 107 4.68 4.48594198444716 4.87405801555284 108 4.68 4.47731301319888 4.88268698680112

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/1wx7s1211974788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/1wx7s1211974788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/2j70v1211974788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/2j70v1211974788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/3mb5w1211974788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211974899jq508k1b7ut1n1n/3mb5w1211974788.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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