exp smoothing eigen reeks - Wouters Danai

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 03:23:27 -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/26/t1211793899wbidkn7k50y6jqc.htm/, Retrieved Mon, 26 May 2008 11:25:03 +0200

User-defined keywords:

Dataseries X:

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3722.7 3707.1 3697.4 3691.4 3679.4 3660.6 3647.5 3639 3623.5 3612.2 3604.2 3596.9 3603.9 3606.9 3607.7 3611.4 3611.9 3618.4 3629.5 3640.6 3646.8 3647.3 3649.5 3649.7 3652.5 3665.8 3674.3 3705.8 3735.8 3735.4 3747.7 3765.5 3779.7 3795.5 3813.1 3826.9 3833.3 3844.8 3851.3 3851.8 3854.1 3858.4 3861.6 3856.3 3855.8 3860.4 3855.1 3839.5 3833 3833.6 3826.8 3818.2 3811.4 3806.8 3810.3 3818.2 3858.7 3868.7 3872.6 3872.4 3876.4 3883.2 3883.4 3881.8 3887.1 3893.3 3902.8 3914.7 3929.8 3947.3 3971.8 3991.3 3993 3997.2 4016.2 4041.7 4060.5 4076.7 4102.7 4125.8 4140.1 4146.7 4157.9 4154.7 4145.3 4149 4142.4 4141 4146.1 4147.6 4142.7 4148.1 4159 4167 4178.5 4192.5 4209.2 4223.7 4231.6 4236.9 4253 4270.5 4285.7 4302.8 4321.5 4340.3 4356.5

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 9 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 3707.1 3722.7 -15.5999999999999 3 3697.4 3707.1 -9.69999999999982 4 3691.4 3697.4 -6 5 3679.4 3691.4 -12 6 3660.6 3679.4 -18.8000000000002 7 3647.5 3660.6 -13.0999999999999 8 3639 3647.5 -8.5 9 3623.5 3639 -15.5 10 3612.2 3623.5 -11.3000000000002 11 3604.2 3612.2 -8 12 3596.9 3604.2 -7.29999999999973 13 3603.9 3596.9 7 14 3606.9 3603.9 3 15 3607.7 3606.9 0.799999999999727 16 3611.4 3607.7 3.70000000000027 17 3611.9 3611.4 0.5 18 3618.4 3611.9 6.5 19 3629.5 3618.4 11.0999999999999 20 3640.6 3629.5 11.0999999999999 21 3646.8 3640.6 6.20000000000027 22 3647.3 3646.8 0.5 23 3649.5 3647.3 2.19999999999982 24 3649.7 3649.5 0.199999999999818 25 3652.5 3649.7 2.80000000000018 26 3665.8 3652.5 13.3000000000002 27 3674.3 3665.8 8.5 28 3705.8 3674.3 31.5 29 3735.8 3705.8 30 30 3735.4 3735.8 -0.400000000000091 31 3747.7 3735.4 12.2999999999997 32 3765.5 3747.7 17.8000000000002 33 3779.7 3765.5 14.1999999999998 34 3795.5 3779.7 15.8000000000002 35 3813.1 3795.5 17.5999999999999 36 3826.9 3813.1 13.8000000000002 37 3833.3 3826.9 6.40000000000009 38 3844.8 3833.3 11.5 39 3851.3 3844.8 6.5 40 3851.8 3851.3 0.5 41 3854.1 3851.8 2.29999999999973 42 3858.4 3854.1 4.30000000000018 43 3861.6 3858.4 3.19999999999982 44 3856.3 3861.6 -5.29999999999973 45 3855.8 3856.3 -0.5 46 3860.4 3855.8 4.59999999999991 47 3855.1 3860.4 -5.30000000000018 48 3839.5 3855.1 -15.5999999999999 49 3833 3839.5 -6.5 50 3833.6 3833 0.599999999999909 51 3826.8 3833.6 -6.79999999999973 52 3818.2 3826.8 -8.60000000000036 53 3811.4 3818.2 -6.79999999999973 54 3806.8 3811.4 -4.59999999999991 55 3810.3 3806.8 3.5 56 3818.2 3810.3 7.89999999999964 57 3858.7 3818.2 40.5 58 3868.7 3858.7 10 59 3872.6 3868.7 3.90000000000009 60 3872.4 3872.6 -0.199999999999818 61 3876.4 3872.4 4 62 3883.2 3876.4 6.79999999999973 63 3883.4 3883.2 0.200000000000273 64 3881.8 3883.4 -1.59999999999991 65 3887.1 3881.8 5.29999999999973 66 3893.3 3887.1 6.20000000000027 67 3902.8 3893.3 9.5 68 3914.7 3902.8 11.8999999999996 69 3929.8 3914.7 15.1000000000004 70 3947.3 3929.8 17.5 71 3971.8 3947.3 24.5 72 3991.3 3971.8 19.5 73 3993 3991.3 1.69999999999982 74 3997.2 3993 4.19999999999982 75 4016.2 3997.2 19 76 4041.7 4016.2 25.5 77 4060.5 4041.7 18.8000000000002 78 4076.7 4060.5 16.1999999999998 79 4102.7 4076.7 26 80 4125.8 4102.7 23.1000000000004 81 4140.1 4125.8 14.3000000000002 82 4146.7 4140.1 6.59999999999945 83 4157.9 4146.7 11.1999999999998 84 4154.7 4157.9 -3.19999999999982 85 4145.3 4154.7 -9.39999999999964 86 4149 4145.3 3.69999999999982 87 4142.4 4149 -6.60000000000036 88 4141 4142.4 -1.39999999999964 89 4146.1 4141 5.10000000000036 90 4147.6 4146.1 1.5 91 4142.7 4147.6 -4.90000000000055 92 4148.1 4142.7 5.40000000000055 93 4159 4148.1 10.8999999999996 94 4167 4159 8 95 4178.5 4167 11.5 96 4192.5 4178.5 14 97 4209.2 4192.5 16.6999999999998 98 4223.7 4209.2 14.5 99 4231.6 4223.7 7.90000000000055 100 4236.9 4231.6 5.29999999999927 101 4253 4236.9 16.1000000000004 102 4270.5 4253 17.5 103 4285.7 4270.5 15.1999999999998 104 4302.8 4285.7 17.1000000000004 105 4321.5 4302.8 18.6999999999998 106 4340.3 4321.5 18.8000000000002 107 4356.5 4340.3 16.1999999999998 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 108 4356.5 4334.76852437071 4378.23147562929 109 4356.5 4325.76705243468 4387.23294756532 110 4356.5 4318.85998008663 4394.14001991337 111 4356.5 4313.03704874142 4399.96295125858 112 4356.5 4307.90694324153 4405.09305675847 113 4356.5 4303.26897335052 4409.73102664948 114 4356.5 4299.00391986244 4413.99608013756 115 4356.5 4295.03410486936 4417.96589513064 116 4356.5 4291.30557311214 4421.69442688786 117 4356.5 4287.77904009501 4425.22095990499 118 4356.5 4284.4248491969 4428.5751508031 119 4356.5 4281.21996017326 4431.78003982674

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/1hl6z1211793798.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/1hl6z1211793798.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/2c24g1211793798.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/2c24g1211793798.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/3ydgr1211793798.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793899wbidkn7k50y6jqc/3ydgr1211793798.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')

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Software written by Ed van Stee & Patrick Wessa

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