Gemiddelde consumptieprijs - broodje - Elisa Somers

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 10:19:18 -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/25/t1211732454hb4h9tpt4dm9fo8.htm/, Retrieved Sun, 25 May 2008 18:20:58 +0200

User-defined keywords:

Dataseries X:

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4,07 4,07 4,08 4,09 4,08 4,09 4,12 4,14 4,14 4,14 4,14 4,14 4,23 4,29 4,32 4,33 4,35 4,35 4,35 4,35 4,36 4,36 4,38 4,4 4,4 4,4 4,43 4,44 4,46 4,47 4,49 4,49 4,57 4,62 4,64 4,66 4,67 4,68 4,72 4,74 4,75 4,76 4,77 4,76 4,77 4,77 4,78 4,81 4,81 4,85 4,92 4,96 4,95 4,96 4,97 5 5 5,01 5,01 5,02 5,04 5,04 5,19 5,22 5,22 5,22 5,24 5,28 5,34 5,36 5,38 5,39 5,41 5,44 5,51 5,55 5,56 5,57 5,58 5,58 5,59 5,61 5,63 5,64 5,64

Text written by user:

Single Multiplicatief

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 4.07 4.07 0 3 4.08 4.07 0.00999999999999979 4 4.09 4.08 0.00999999999999979 5 4.08 4.09 -0.00999999999999979 6 4.09 4.08 0.00999999999999979 7 4.12 4.09 0.0300000000000002 8 4.14 4.12 0.0199999999999996 9 4.14 4.14 0 10 4.14 4.14 0 11 4.14 4.14 0 12 4.14 4.14 0 13 4.23 4.14 0.0900000000000007 14 4.29 4.23 0.0599999999999996 15 4.32 4.29 0.0300000000000002 16 4.33 4.32 0.00999999999999979 17 4.35 4.33 0.0199999999999996 18 4.35 4.35 0 19 4.35 4.35 0 20 4.35 4.35 0 21 4.36 4.35 0.0100000000000007 22 4.36 4.36 0 23 4.38 4.36 0.0199999999999996 24 4.4 4.38 0.0200000000000005 25 4.4 4.4 0 26 4.4 4.4 0 27 4.43 4.4 0.0299999999999994 28 4.44 4.43 0.0100000000000007 29 4.46 4.44 0.0199999999999996 30 4.47 4.46 0.00999999999999979 31 4.49 4.47 0.0200000000000005 32 4.49 4.49 0 33 4.57 4.49 0.08 34 4.62 4.57 0.0499999999999998 35 4.64 4.62 0.0199999999999996 36 4.66 4.64 0.0200000000000005 37 4.67 4.66 0.00999999999999979 38 4.68 4.67 0.00999999999999979 39 4.72 4.68 0.04 40 4.74 4.72 0.0200000000000005 41 4.75 4.74 0.00999999999999979 42 4.76 4.75 0.00999999999999979 43 4.77 4.76 0.00999999999999979 44 4.76 4.77 -0.00999999999999979 45 4.77 4.76 0.00999999999999979 46 4.77 4.77 0 47 4.78 4.77 0.0100000000000007 48 4.81 4.78 0.0299999999999994 49 4.81 4.81 0 50 4.85 4.81 0.04 51 4.92 4.85 0.0700000000000003 52 4.96 4.92 0.04 53 4.95 4.96 -0.00999999999999979 54 4.96 4.95 0.00999999999999979 55 4.97 4.96 0.00999999999999979 56 5 4.97 0.0300000000000002 57 5 5 0 58 5.01 5 0.00999999999999979 59 5.01 5.01 0 60 5.02 5.01 0.00999999999999979 61 5.04 5.02 0.0200000000000005 62 5.04 5.04 0 63 5.19 5.04 0.150000000000000 64 5.22 5.19 0.0299999999999994 65 5.22 5.22 0 66 5.22 5.22 0 67 5.24 5.22 0.0200000000000005 68 5.28 5.24 0.04 69 5.34 5.28 0.0599999999999996 70 5.36 5.34 0.0200000000000005 71 5.38 5.36 0.0199999999999996 72 5.39 5.38 0.00999999999999979 73 5.41 5.39 0.0200000000000005 74 5.44 5.41 0.0300000000000002 75 5.51 5.44 0.0699999999999994 76 5.55 5.51 0.04 77 5.56 5.55 0.00999999999999979 78 5.57 5.56 0.0100000000000007 79 5.58 5.57 0.00999999999999979 80 5.58 5.58 0 81 5.59 5.58 0.00999999999999979 82 5.61 5.59 0.0200000000000005 83 5.63 5.61 0.0199999999999996 84 5.64 5.63 0.00999999999999979 85 5.64 5.64 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 5.64 5.59162787205843 5.68837212794157 87 5.64 5.57159148062419 5.70840851937581 88 5.64 5.55621701673499 5.72378298326501 89 5.64 5.54325574411687 5.73674425588313 90 5.64 5.53183663370634 5.74816336629366 91 5.64 5.52151296877054 5.75848703122946 92 5.64 5.51201937907962 5.76798062092038 93 5.64 5.50318296124838 5.77681703875162 94 5.64 5.4948836161753 5.7851163838247 95 5.64 5.48703390043558 5.79296609956442 96 5.64 5.47956780130676 5.80043219869324 97 5.64 5.47243403346997 5.80756596653003

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/10cow1211732351.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/10cow1211732351.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/2trnt1211732351.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/2trnt1211732351.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/3fpks1211732351.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211732454hb4h9tpt4dm9fo8/3fpks1211732351.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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')

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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