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trubador wrote:Lambdas are the coefficents of variances in the mean equations.

PERRYGOGAS wrote:So other than the singular matrix problem that is data driven the program seems to work in this form?

trubador wrote:The error you detected should be corrected as the way you did. I checked the log-likelihood specification and it is correct. So you do not have to worry about the rest of the code. Final version of the code after your modifications seems allright and therefore you should now be able to estimate a bivariate GARCH-M model. If you encounter any further problems, we can work on them as well.

If you had some experience on any other programming language or software package, then you could easily learn EViews. I can assure you that you will reap the benefits with little patience. Although the programming language of EViews is different than that of RATS, it really increases the flexibility with its ease of use. RATS is extremely command-driven, which I believe gives the ability to perform difficult tasks via writing procedures or using the built-in ones. Therefore, it has a wider range of applications. On the other hand, commands and programming language are interestingly similar (in narrow sense) between EViews and MATLAB. Hopefully, in the near future QMS will broaden the area of use of EViews via adding new features and improving the current ones.

yaser wrote:dear trubador
I have applied this code and its working, however I can not add AR elements to the mean equation, actually it needs to be a VAR with two lags.

how can I add lag variables to the mean equation?

mamo1 wrote:Hi all,
Like many of you I am working on my thesis and I need to estimate bi-variate BEKK-GARCH(1,1). I looked into the sample code and it restricts the variance covariance matrix to diagonals. Can someone, please, help me modify the code so that it will do the following:

y1 = a0 + a1*x1 + a2*var(y1) + a3*cov(y1, y2)
y2 = b0 + b1*x2 + b2*var(y2) + b3*cov(y1, y2)

where x1 and x2 are exogenous variables. And beta, alpha in {H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha'} are not restricted to be diagonals.

Thank you in advance for taking your time.
Mamo,

trubador wrote:Yes, there is actually. I strongly agree with you that such recursive estimations lead to false or inconsistent results and joint estimation methods should be preferred where possible. You can build a multivariate garch in mean framework in EViews and estimate it easily with LogL object. Besides, you do not need to write a program from scratch and all you have to do is modify a sample program of trivariate garch provided by EViews (the path is ...\EViews6\Example Files\Sample Programs\logl\tv_garch.prg). Although it will be a tedious attempt for models with more than three variables, you can still alter the code to suit your problem.

Please note that original code provided by EViews also contains some small errors. I corrected and showed them as well. And there may also be further errors in the original code and in my modifications. So please check carefully before using it!

As an example, I made the following modifications for the trivariate garch in mean model:

'........ (means rest of the steps are same as the original version of the code)

Code: Select all

'........
' y = mu + lambda*H + res
'........
'  where,
'........
'    lambda = 3 x 1
'........
'get starting values from univariate GARCH
equation eq1.arch(archm=var,m=100,c=1e-5) y1 c
equation eq2.arch(archm=var,m=100,c=1e-5) y2 c
equation eq3.arch(archm=var,m=100,c=1e-5) y3 c

'save the conditional variances
eq1.makegarch garch1
eq2.makegarch garch2
eq3.makegarch garch3
'........
' declare coef vectors to use in GARCH model
coef(3) lambda 'please note that c(1) now belongs to conditional variance in the mean equation and do not forget to change other coefficients accordingly.
lambda(1) = eq1.c(1)
lambda(2) = eq2.c(1)
lambda(3) = eq3.c(1)
'........
 mu(3) = eq3.c(2) 'in the original specification equation number is misspecified
'........
 alpha(3) = (eq3.c(4))^.5 'in the original specification equation number is misspecified
'........
' use sample var-cov as starting value of variance-covariance matrix
series cov_y1y2 = @cov(y1-mu(1)-lambda(1)*garch1, y2-mu(2)-lambda(2)*garch2)
series cov_y1y3 = @cov(y1-mu(1)-lambda(1)*garch1, y3-mu(3)-lambda(3)*garch3)
series cov_y2y3 = @cov(y2-mu(2)-lambda(2)*garch2, y3-mu(3)-lambda(3)*garch3)
series var_y1 = @var(y1-lambda(1)*garch1)
series var_y2 = @var(y2-lambda(2)*garch2)
series var_y3 = @var(y3-lambda(3)*garch3)

series sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
series sqres2 = (y2-mu(2)-lambda(2)*garch2)^2
series sqres3 = (y3-mu(3)-lambda(3)*garch3)^2

series res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)
series res1res3 = (y1-mu(1)-lambda(1)*garch1)*(y3-mu(3)-lambda(3)*garch3)
series res2res3 = (y2-mu(2)-lambda(2)*garch2)*(y3-mu(3)-lambda(3)*garch3)
'........
' squared errors and cross errors
tvgarch.append @logl logl
tvgarch.append sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
tvgarch.append sqres2 = (y2-mu(2)-lambda(2)*garch2)^2
tvgarch.append sqres3 = (y3-mu(3)-lambda(3)*garch3)^2

tvgarch.append res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)
tvgarch.append res1res3 = (y1-mu(1)-lambda(1)*garch1)*(y3-mu(3)-lambda(3)*garch3)
tvgarch.append res2res3 = (y2-mu(2)-lambda(2)*garch2)*(y3-mu(3)-lambda(3)*garch3)
'........