| 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 |