TSECCTEST Procedure

@TSECCTEST performs the Tse(2000) LM test for CC in multivariate GARCH models. This tests the adequacy of a CC representation for the covariances in a GARCH model.

@TSECCTEST( options ) (no parameters)

Options

RVECTOR=SERIES[VECTOR] of GARCH residuals

HMAT=SERIES[SYMM] of GARCH covariance matrices

DERIVES=VECT[SERIES] of GARCH gradient components

These need to come from the GARCH instruction estimated with MV=CC.

TITLE="title for test" ["Tse Test for CC"]

[PRINT]/NOPRINT

Variables Defined

%CDSTAT	the LM test statistic (REAL)
%SIGNIF	the significance level as a chi-square with n(n-1)/2 d.f. (REAL)

Setup

To use the procedure, first use GARCH with MV=CC. Note that the GARCH model cannot use off-diagonal covariances in either the mean or variance models. The use of variances is OK, so you can have an "M" model which uses variances, but not the covariances. In estimating the original model, you need to save the following (which are required inputs into this procedure):

1.The residuals. Save with the RVECTOR option on GARCH; input using the RVECTOR option on the procedure.

2.The covariance matrices. Save with the HMAT option on GARCH; input using the HMAT option on the procedure.

3.The derivatives of the log likelihood elements with respect to the parameters. Save with the DERIVES option on GARCH; input using the DERIVES option on the procedure.

Example

* Tse LM test for constant correlation. Replicates results in Tse, Y.

* K.(2000), "A Test for Constant Correlations in a Multivariate GARCH

* Model", Journal of Econometrics 98, 107-127.

* Revision Schedule:

* 07/2005 Rewritten to use GARCH instruction

* 08/2010 Rewritten to use TseCCTest procedure

all 812

open data exratew.dat

data(format=free,org=columns) / malaysia singapore

* This is an LM test for CC-GARCH versus the specific alternative:

* rho(i,j)(t)=rho(i,j)+delta(i,j)*e(i)(t-1)e(j)(t-1)

* at delta=0, which will give the CC estimates.

* In order to use the TseCCTest procedure, you must estimate a GARCH

* model with MV=CC and save the residuals (using RVECTOR), the

* covariance matrices (using HMAT) and the gradient elements (using

* DERIVES).

* In order to apply the Tse test (in this form), the model can't use the

* (off-diagonal) covariances in any form elsewhere in the model. So, for

* instance, you can't use any "M" specification which use covariances

* and not just variances.

garch(p=1,q=1,nomean,mv=cc,derives=ccderives,rvector=uv,hmat=h) / malaysia singapore

@tsecctest(derives=ccderives,hmat=h,rvector=uv)

Sample Output

Tse Test for CC

Chi-Squared(1)= 2.618589 with Significance Level 0.10561835