Library: | times |
See also: | archest archtest genarch rvlm |
Quantlet: | bigarch | |
Description: | estimates the BEKK (Baba, Engle, Kraft, Kroner) volatility representation for a bivariate conditionally heteroscedastic time series and evaluates the maximum of the quasi log likelihood function in a GARCH(1,1) frame of the following form: S_t=C_(0)^T*C_(0)+A_(11)^T*e_(t-1)*e_(t-1)^T*A_(11)+G_(11)^T* S_(t-1)*G_(11) |
Usage: | {th,liks}=bigarch(theta,et) | |
Input: | ||
theta | columns of 2x2 ARCH and GARCH parameter matrices | |
et | T x 2 matrix containing the time series data | |
Output: | ||
th | elements of the upper triangular 2x2 matrix of the deterministic variance components and estimated columns of 2x2 ARCH and GARCH parameter matrices | |
liks | evaluated log likelihood function |
library("times") theta=#(0.5, 0.01, 0.01, 0.5, 0.6, 0.01, 0.01, 0.7) et=read("bigarch") {th, liks} = bigarch(theta, et) th liks
Contents of th [ 1,] 0.66929 [ 2,] 0.10183 [ 3,] 0.026132 [ 4,] 0.37569 [ 5,] 0.20174 [ 6,] -0.2142 [ 7,] 0.28792 [ 8,] -0.011575 [ 9,] -0.02021 [10,] 0.47874 [11,] 0.72634 Contents of liks [1,] 1035.7
library("xplore") library("stats") library("times") ; read the data et1=read("fx") dat1=tdiff(log(et1[,1])) dat2=tdiff(log(et1[,2])) dat=dat1~dat2 a=1:dim(dat1) b=1:dim(dat2) dat1gr=a~dat1 dat2gr=b~dat2 fxrate="DEM/GBP"|"DEM/USD" ; summary statistics summarize(dat1~dat2, fxrate) disp=createdisplay(2,1) setmaskp(dat1gr,1,1,0) setmaskl(dat1gr,a',1,1,1) setmaskp(dat2gr,1,1,0) setmaskl(dat2gr,b',1,1,1) show(disp,1,1,dat1gr) show(disp,2,1,dat2gr) setgopt(disp,1,1,"xlabel", "Time", "title", "Foreign exchange rate returns: DEM/USD","yvalue",0|1) setgopt(disp,2,1,"xlabel", "Time", "title", "Foreign exchange rate returns: DEM/GBP","yvalue",0|1) ; fix starting values theta=#(0.28,-0.06,-0.05, 0.2, 0.9, 0.03, 0.02, 0.9) ;call bigarch {coeff, maxlik} = bigarch(theta, dat) coeff maxlik
Contents of summ [1,] " " [2,] " Minimum Maximum Mean Median Std.Error" [3,] " -------------------------------------------------------------" [4,] "DEM/GBP -0.040125 0.031874 -4.7184e-06 0 0.0070936" [5,] "DEM/USD -0.046682 0.038665 0.00011003 0 0.0069721" [6,] " " Contents of coeff [ 1,] 0.0011516 [ 2,] 0.00031009 [ 3,] 0.00075685 [ 4,] 0.28185 [ 5,] -0.057194 [ 6,] -0.050449 [ 7,] 0.29344 [ 8,] 0.93878 [ 9,] 0.025117 [10,] 0.027503 [11,] 0.9391 Contents of maxlik [1,] -28599 According to the model setup outlined above the results can be expressed by the following matrices: C_(0) = |0.0011519 0.0031009| | 0 0.0075685| A_(11)= |0.28185 -0.050449| |-0.057194 0.29344 | G_(11)= |0.93878 0.025117| |0.027503 0.9391 |