HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

For technical questions regarding estimation of single equations, systems, VARs, Factor analysis and State Space Models in EViews. General econometric questions and advice should go in the Econometric Discussions forum.

Moderators: EViews Gareth, EViews Moderator

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Fri Dec 26, 2008 4:36 pm

Is there a way to do this? there is no option in Eviews, but some other
manual way of doing it within the multivariate GARCH (VECH) estimation
framework?

And not this:
1) estimating a GARCH model first without conditional variance in the mean equation
2) generate the conditional variance
3) next create another GARCH system, this time place the conditional variance terms from the first system in the mean equations
4) estimate this system
5) generate the conditional variance with the same name as the first time
6) repeat 4) and 5) until no improvement in model criteria (log likelihood, AIC, etc.)

This will lead to the generated regressors problem!

trubador
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby trubador » Sat Dec 27, 2008 6:18 am

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)
'........

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Sat Dec 27, 2008 12:35 pm

Thank you for the reply and help. Is the program you refer to a trivariate GARCH-M?
I am only going to use a bivariate model for now.

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Sat Dec 27, 2008 3:49 pm

Tried the tv_garch program but I think it is nothing like the one above:

Code: Select all

@LOGL LOGL
SQRES1 = (Y1-MU(1))^2
SQRES2 = (Y2-MU(2))^2
SQRES3 = (Y3-MU(3))^2
RES1RES2 = (Y1-MU(1))*(Y2-MU(2))
RES1RES3 = (Y1-MU(1))*(Y3-MU(3))
RES2RES3 = (Y3-MU(3))*(Y2-MU(2))
VAR_Y1  =  OMEGA(1)^2 + BETA(1)^2*VAR_Y1(-1) + ALPHA(1)^2*SQRES1(-1)
VAR_Y2  = OMEGA(2)^2+OMEGA(4)^2 + BETA(2)^2*VAR_Y2(-1) + ALPHA(2)^2*SQRES2(-1)
VAR_Y3  = OMEGA(3)^2+OMEGA(5)^2+OMEGA(6)^2 + BETA(3)^2*VAR_Y3(-1) + ALPHA(3)^2*SQRES3(-1)
COV_Y1Y2 = OMEGA(1)*OMEGA(2) + BETA(2)*BETA(1)*COV_Y1Y2(-1) + ALPHA(2)*ALPHA(1)*RES1RES2(-1)
COV_Y1Y3 = OMEGA(1)*OMEGA(3) + BETA(3)*BETA(1)*COV_Y1Y3(-1) + ALPHA(3)*ALPHA(1)*RES1RES3(-1)
COV_Y2Y3 = OMEGA(2)*OMEGA(3) + OMEGA(4)*OMEGA(5) + BETA(3)*BETA(2)*COV_Y2Y3(-1) + ALPHA(3)*ALPHA(2)*RES2RES3(-1)
DETH = VAR_Y1*VAR_Y2*VAR_Y3 - VAR_Y1*COV_Y2Y3^2-COV_Y1Y2^2*VAR_Y3+2*COV_Y1Y2*COV_Y2Y3*COV_Y1Y3-COV_Y1Y3^2*VAR_Y2
INVH1 = (VAR_Y2*VAR_Y3-COV_Y2Y3^2)/DETH
INVH2 = -(COV_Y1Y2*VAR_Y3-COV_Y1Y3*COV_Y2Y3)/DETH
INVH3 = (COV_Y1Y2*COV_Y2Y3-COV_Y1Y3*VAR_Y2)/DETH
INVH4 = (VAR_Y1*VAR_Y3-COV_Y1Y3^2)/DETH
INVH5 = -(VAR_Y1*COV_Y2Y3-COV_Y1Y2*COV_Y1Y3)/DETH
INVH6 = (VAR_Y1*VAR_Y2-COV_Y1Y2^2)/DETH
LOGL = -0.5*(5.51363119922804 + (INVH1*SQRES1+INVH4*SQRES2+INVH6*SQRES3 +2*INVH2*RES1RES2 +2*INVH3*RES1RES3+2*INVH5*RES2RES3 ) + LOG(DETH))

trubador
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby trubador » Sun Dec 28, 2008 6:02 am

The code that I modified belongs to the version 6 of EViews and worked well after the modifications I made. Therefore, there may be some differences with earlier versions. However, the logic will be the same and you should adjust the variables accordingly. Plus, you are willing to conduct a bivariate analysis that make things much easier for you. The log likelihood of bivariate model is more parsimonious, and still you do not have write your own because there is also a sample program in EViews written for bivariate garch analysis. If you cannot find it or still have problems just let me know...

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Tue Dec 30, 2008 6:08 pm

Dear trubador,

Thank you for the help and thank you for your patience. I am using Eviews 6 as well. I will use the bivariate GARCH program then, but having limited experience with programming EVIEWS I do not know how to include the GARCH variance or standard deviation in the mean equation.

This is the program I find in EVIEWS programs folder:

Code: Select all

' BV_GARCH.PRG (3/30/2004)
' Revised for 6.0 (3/7/2007)
' example program for EViews LogL object
'
' restricted version of
' bi-variate BEKK of Engle and Kroner (1995):
'
'  y = mu + res
'  res ~ N(0,H)
'
'  H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha'
'
' where
'
'     y = 2 x 1
'     mu = 2 x 1
'      H = 2 x 2 (symmetric)
'          H(1,1) = variance of y1   (saved as var_y1)
'          H(1,2) = cov of y1 and y2 (saved as var_y2)
'          H(2,2) = variance of y2   (saved as cov_y1y2)
'  omega = 2 x 2 low triangular
'   beta = 2 x 2 diagonal
'  alpha = 2 x 2 diagonal
'

'change path to program path
%path = @runpath
cd %path

' load workfile
load intl_fin.wf1

' dependent variables of both series must be continues
smpl @all
series y1 = dlog(sp500)
series y2 = dlog(tbond)

' set sample
' first observation of s1 need to be one or two periods after
' the first observation of s0
sample s0 3/1/1994 8/25/2000
sample s1 3/2/1994 8/25/2000


' initialization of parameters and starting values
' change below only to change the specification of model
smpl s0

'get starting values from univariate GARCH
equation eq1.arch(m=100,c=1e-5) y1 c
equation eq2.arch(m=100,c=1e-5) y2 c

' declare coef vectors to use in bi-variate GARCH model
' see above for details
coef(2) mu
 mu(1) = eq1.c(1)
 mu(2)= eq2.c(1)

coef(3) omega
 omega(1)=(eq1.c(2))^.5
 omega(2)=0
 omega(3)=eq2.c(2)^.5

coef(2) alpha
 alpha(1) = (eq1.c(3))^.5
 alpha(2) = (eq2.c(3))^.5

coef(2) beta
 beta(1)= (eq1.c(4))^.5
 beta(2)= (eq2.c(4))^.5

' constant adjustment for log likelihood
!mlog2pi = 2*log(2*@acos(-1))

' use var-cov of sample in "s1" as starting value of variance-covariance matrix
series cov_y1y2 = @cov(y1-mu(1), y2-mu(2))
series var_y1 = @var(y1)
series var_y2 = @var(y2)

series sqres1 = (y1-mu(1))^2
series sqres2 = (y2-mu(2))^2
series res1res2 = (y1-mu(1))*(y2-mu(2))


' ...........................................................
' LOG LIKELIHOOD
' set up the likelihood
' 1) open a new blank likelihood object (L.O.) name bvgarch
' 2) specify the log likelihood model by append
' ...........................................................

logl bvgarch
bvgarch.append @logl logl
bvgarch.append sqres1 = (y1-mu(1))^2
bvgarch.append sqres2 = (y2-mu(2))^2
bvgarch.append res1res2 = (y1-mu(1))*(y2-mu(2))

' calculate the variance and covariance series
bvgarch.append var_y1  =  omega(1)^2 + beta(1)^2*var_y1(-1) + alpha(1)^2*sqres1(-1)
bvgarch.append var_y2  = omega(3)^2+omega(2)^2 + beta(2)^2*var_y2(-1) + alpha(2)^2*sqres2(-1)
bvgarch.append cov_y1y2 = omega(1)*omega(2) + beta(2)*beta(1)*cov_y1y2(-1) + alpha(2)*alpha(1)*res1res2(-1)

' determinant of the variance-covariance matrix
bvgarch.append deth = var_y1*var_y2 - cov_y1y2^2

' inverse elements of the variance-covariance matrix
bvgarch.append invh1 = var_y2/deth
bvgarch.append invh3 = var_y1/deth
bvgarch.append invh2 = -cov_y1y2/deth

' log-likelihood series
bvgarch.append logl =-0.5*(!mlog2pi + (invh1*sqres1+2*invh2*res1res2+invh3*sqres2) + log(deth))

' remove some of the intermediary series
' bvgarch.append @temp invh1 invh2 invh3 sqres1 sqres2 res1res2 deth


' estimate the model
smpl s1
bvgarch.ml(showopts, m=100, c=1e-5)

' change below to display different output
show bvgarch.output
graph varcov.line var_y1 var_y2 cov_y1y2
show varcov

' LR statistic for univariate versus bivariate model
scalar lr = -2*( eq1.@logl + eq2.@logl - bvgarch.@logl )
scalar lr_pval = 1 - @cchisq(lr,1)


trubador
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby trubador » Wed Dec 31, 2008 1:13 am

Below you can find similar modifications for bivariate GARCH-M model:

Code: Select all

'............
'  y = mu + H*lambda + res

'............

'     lambda = 2 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

'save the conditional variances
eq1.makegarch garch1
eq2.makegarch garch2

'............

' declare coef vectors to use in GARCH model
coef(2) lambda
 lambda(1) = eq1.c(1)
 lambda(2) = eq2.c(1)

coef(2) mu
 mu(1) = eq1.c(2)
 mu(2)= eq2.c(2)

coef(3) omega
 omega(1)=(eq1.c(3))^.5
 omega(2)=0
 omega(3)=eq2.c(3)^.5

coef(2) alpha
 alpha(1) = (eq1.c(4))^.5
 alpha(2) = (eq2.c(4))^.5

coef(2) beta
 beta(1)= (eq1.c(5))^.5
 beta(2)= (eq2.c(5))^.5

'............

' 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 var_y1 = @var(y1-lambda(1)*garch1)
series var_y2 = @var(y2-lambda(2)*garch2)

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

series res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)

'............

' squared errors and cross errors
bvgarch.append @logl logl
bvgarch.append sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
bvgarch.append sqres2 = (y2-mu(2)-lambda(2)*garch2)^2

bvgarch.append res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)
'............


You can copy and paste the modified pieces and replace them in the original code. I do not send you the whole code to highlight and help you better understand the modifications. If you have any problems, please do not hesitate to contact...

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Mon Jan 05, 2009 9:24 am

In the original code I see that in the notes the variances are defined wrong:


' H(1,1) = variance of y1 (saved as var_y1)
' H(1,2) = cov of y1 and y2 (saved as var_y2)
' H(2,2) = variance of y2 (saved as cov_y1y2)

They should be cov_y1y2 and var_y2 respectively. Hope this does not carry down
to the estimation.

PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Mon Jan 05, 2009 9:51 am

Dear tubador,

I have modified the program as below. Hope it is OK now. The programming language of
EVIEWS looks a bit strange to me and not very intuitive. I have had experience with RATS
etc. and I find this much different. Maybe there is a steep learning curve for this.

If you could take a look and tell me what you think it would be great!
Thank you again,
Perry

Code: Select all

' BV_GARCH.PRG (3/30/2004)
' Revised for 6.0 (3/7/2007)
' example program for EViews LogL object
'
' restricted version of
' bi-variate BEKK of Engle and Kroner (1995):
'
'  y = mu + res -> y = mu + H*lambda + res
'  res ~ N(0,H)
'
'  H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha'
'
' where
'
'     y = 2 x 1
'     mu = 2 x 1
'    -> lambda = 2 x 1
'      H = 2 x 2 (symmetric)
'          H(1,1) = variance of y1   (saved as var_y1)
'          H(1,2) = cov of y1 and y2 (saved as var_y2)
'          H(2,2) = variance of y2   (saved as cov_y1y2)
'  omega = 2 x 2 low triangular
'   beta = 2 x 2 diagonal
'  alpha = 2 x 2 diagonal
'

'change path to program path
%path = @runpath
cd %path

' load workfile
load intl_fin.wf1

' dependent variables of both series must be continues
smpl @all
series y1 = dlog(sp500)
series y2 = dlog(tbond)

' set sample
' first observation of s1 need to be one or two periods after
' the first observation of s0
sample s0 3/1/1994 8/25/2000
sample s1 3/2/1994 8/25/2000


' initialization of parameters and starting values
' change below only to change the specification of model
smpl s0

'get starting values from univariate GARCH
'equation eq1.arch(m=100,c=1e-5) y1 c
'equation eq2.arch(m=100,c=1e-5) y2 c

equation eq1.arch(archm=var,m=100,c=1e-5) y1 c
equation eq2.arch(archm=var,m=100,c=1e-5) y2 c

'save the conditional variances
eq1.makegarch garch1
eq2.makegarch garch2


' declare coef vectors to use in bi-variate GARCH model
' see above for details
'coef(2) mu
' mu(1) = eq1.c(1)
' mu(2)= eq2.c(1)

'coef(3) omega
' omega(1)=(eq1.c(2))^.5
' omega(2)=0
' omega(3)=eq2.c(2)^.5

'coef(2) alpha
' alpha(1) = (eq1.c(3))^.5
' alpha(2) = (eq2.c(3))^.5

'coef(2) beta
' beta(1)= (eq1.c(4))^.5
' beta(2)= (eq2.c(4))^.5

'new values
    ' declare coef vectors to use in GARCH model
    coef(2) lambda
    lambda(1) = eq1.c(1)
    lambda(2) = eq2.c(1)

    coef(2) mu
    mu(1) = eq1.c(2)
    mu(2)= eq2.c(2)

    coef(3) omega
    omega(1)=(eq1.c(3))^.5
    omega(2)=0
    omega(3)=eq2.c(3)^.5

    coef(2) alpha
    alpha(1) = (eq1.c(4))^.5
    alpha(2) = (eq2.c(4))^.5

    coef(2) beta
    beta(1)= (eq1.c(5))^.5
    beta(2)= (eq2.c(5))^.5





' constant adjustment for log likelihood
!mlog2pi = 2*log(2*@acos(-1))

'old values
' use var-cov of sample in "s1" as starting value of variance-covariance matrix
'series cov_y1y2 = @cov(y1-mu(1), y2-mu(2))
'series var_y1 = @var(y1)
'series var_y2 = @var(y2)

'series sqres1 = (y1-mu(1))^2
'series sqres2 = (y2-mu(2))^2
'series res1res2 = (y1-mu(1))*(y2-mu(2))

    series cov_y1y2 = @cov(y1-mu(1)-lambda(1)*garch1, y2-mu(2)-lambda(2)*garch2)

    series var_y1 = @var(y1-lambda(1)*garch1)
    series var_y2 = @var(y2-lambda(2)*garch2)

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

    series res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)



' ...........................................................
' LOG LIKELIHOOD
' set up the likelihood
' 1) open a new blank likelihood object (L.O.) name bvgarch
' 2) specify the log likelihood model by append
' ...........................................................

logl bvgarch
'old values
'bvgarch.append @logl logl
'bvgarch.append sqres1 = (y1-mu(1))^2
'bvgarch.append sqres2 = (y2-mu(2))^2
'bvgarch.append res1res2 = (y1-mu(1))*(y2-mu(2))

    ' squared errors and cross errors
    bvgarch.append @logl logl
    bvgarch.append sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
    bvgarch.append sqres2 = (y2-mu(2)-lambda(2)*garch2)^2

    bvgarch.append res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)


' calculate the variance and covariance series
bvgarch.append var_y1  =  omega(1)^2 + beta(1)^2*var_y1(-1) + alpha(1)^2*sqres1(-1)
bvgarch.append var_y2  = omega(3)^2+omega(2)^2 + beta(2)^2*var_y2(-1) + alpha(2)^2*sqres2(-1)
bvgarch.append cov_y1y2 = omega(1)*omega(2) + beta(2)*beta(1)*cov_y1y2(-1) + alpha(2)*alpha(1)*res1res2(-1)

' determinant of the variance-covariance matrix
bvgarch.append deth = var_y1*var_y2 - cov_y1y2^2

' inverse elements of the variance-covariance matrix
bvgarch.append invh1 = var_y2/deth
bvgarch.append invh3 = var_y1/deth
bvgarch.append invh2 = -cov_y1y2/deth

' log-likelihood series
bvgarch.append logl =-0.5*(!mlog2pi + (invh1*sqres1+2*invh2*res1res2+invh3*sqres2) + log(deth))

' remove some of the intermediary series
' bvgarch.append @temp invh1 invh2 invh3 sqres1 sqres2 res1res2 deth


' estimate the model
smpl s1
bvgarch.ml(showopts, m=100, c=1e-5)

' change below to display different output
show bvgarch.output
graph varcov.line var_y1 var_y2 cov_y1y2
show varcov

' LR statistic for univariate versus bivariate model
scalar lr = -2*( eq1.@logl + eq2.@logl - bvgarch.@logl )
scalar lr_pval = 1 - @cchisq(lr,1)


PERRYGOGAS
Posts: 32
Joined: Sat Nov 01, 2008 12:22 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby PERRYGOGAS » Mon Jan 05, 2009 10:02 am

Am I right that the above program will estimate a multivariate GARCH-M where
the explanatory variables in the mean equations are only the constants (mu) and
the lagged GARCH term?

trubador
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby trubador » Mon Jan 05, 2009 1:38 pm

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.
Last edited by trubador on Mon Jan 05, 2009 2:22 pm, edited 1 time in total.

EViews Gareth
Fe ddaethom, fe welon, fe amcangyfrifon
Posts: 11549
Joined: Tue Sep 16, 2008 5:38 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby EViews Gareth » Mon Jan 05, 2009 2:07 pm

trubador wrote: Hopefully, in the near future QMS will broaden the area of use of EViews via adding new features and improving the current ones.


That's certainly our plan. Of course any suggestions/requests for specific features would be greatly appreciated.
Follow us on Twitter @IHSEViews

yaser
Posts: 9
Joined: Tue Nov 23, 2010 9:49 am

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby yaser » Wed Dec 01, 2010 1:55 am

I used this code, but I don't find any in mean element i the final estimation result
there shouldn't be or there is and I can't find it?

PERRYGOGAS wrote:Dear tubador,

I have modified the program as below. Hope it is OK now. The programming language of
EVIEWS looks a bit strange to me and not very intuitive. I have had experience with RATS
etc. and I find this much different. Maybe there is a steep learning curve for this.

If you could take a look and tell me what you think it would be great!
Thank you again,
Perry

Code: Select all

' BV_GARCH.PRG (3/30/2004)
' Revised for 6.0 (3/7/2007)
' example program for EViews LogL object
'
' restricted version of
' bi-variate BEKK of Engle and Kroner (1995):
'
'  y = mu + res -> y = mu + H*lambda + res
'  res ~ N(0,H)
'
'  H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha'
'
' where
'
'     y = 2 x 1
'     mu = 2 x 1
'    -> lambda = 2 x 1
'      H = 2 x 2 (symmetric)
'          H(1,1) = variance of y1   (saved as var_y1)
'          H(1,2) = cov of y1 and y2 (saved as var_y2)
'          H(2,2) = variance of y2   (saved as cov_y1y2)
'  omega = 2 x 2 low triangular
'   beta = 2 x 2 diagonal
'  alpha = 2 x 2 diagonal
'

'change path to program path
%path = @runpath
cd %path

' load workfile
load intl_fin.wf1

' dependent variables of both series must be continues
smpl @all
series y1 = dlog(sp500)
series y2 = dlog(tbond)

' set sample
' first observation of s1 need to be one or two periods after
' the first observation of s0
sample s0 3/1/1994 8/25/2000
sample s1 3/2/1994 8/25/2000


' initialization of parameters and starting values
' change below only to change the specification of model
smpl s0

'get starting values from univariate GARCH
'equation eq1.arch(m=100,c=1e-5) y1 c
'equation eq2.arch(m=100,c=1e-5) y2 c

equation eq1.arch(archm=var,m=100,c=1e-5) y1 c
equation eq2.arch(archm=var,m=100,c=1e-5) y2 c

'save the conditional variances
eq1.makegarch garch1
eq2.makegarch garch2


' declare coef vectors to use in bi-variate GARCH model
' see above for details
'coef(2) mu
' mu(1) = eq1.c(1)
' mu(2)= eq2.c(1)

'coef(3) omega
' omega(1)=(eq1.c(2))^.5
' omega(2)=0
' omega(3)=eq2.c(2)^.5

'coef(2) alpha
' alpha(1) = (eq1.c(3))^.5
' alpha(2) = (eq2.c(3))^.5

'coef(2) beta
' beta(1)= (eq1.c(4))^.5
' beta(2)= (eq2.c(4))^.5

'new values
    ' declare coef vectors to use in GARCH model
    coef(2) lambda
    lambda(1) = eq1.c(1)
    lambda(2) = eq2.c(1)

    coef(2) mu
    mu(1) = eq1.c(2)
    mu(2)= eq2.c(2)

    coef(3) omega
    omega(1)=(eq1.c(3))^.5
    omega(2)=0
    omega(3)=eq2.c(3)^.5

    coef(2) alpha
    alpha(1) = (eq1.c(4))^.5
    alpha(2) = (eq2.c(4))^.5

    coef(2) beta
    beta(1)= (eq1.c(5))^.5
    beta(2)= (eq2.c(5))^.5





' constant adjustment for log likelihood
!mlog2pi = 2*log(2*@acos(-1))

'old values
' use var-cov of sample in "s1" as starting value of variance-covariance matrix
'series cov_y1y2 = @cov(y1-mu(1), y2-mu(2))
'series var_y1 = @var(y1)
'series var_y2 = @var(y2)

'series sqres1 = (y1-mu(1))^2
'series sqres2 = (y2-mu(2))^2
'series res1res2 = (y1-mu(1))*(y2-mu(2))

    series cov_y1y2 = @cov(y1-mu(1)-lambda(1)*garch1, y2-mu(2)-lambda(2)*garch2)

    series var_y1 = @var(y1-lambda(1)*garch1)
    series var_y2 = @var(y2-lambda(2)*garch2)

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

    series res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)



' ...........................................................
' LOG LIKELIHOOD
' set up the likelihood
' 1) open a new blank likelihood object (L.O.) name bvgarch
' 2) specify the log likelihood model by append
' ...........................................................

logl bvgarch
'old values
'bvgarch.append @logl logl
'bvgarch.append sqres1 = (y1-mu(1))^2
'bvgarch.append sqres2 = (y2-mu(2))^2
'bvgarch.append res1res2 = (y1-mu(1))*(y2-mu(2))

    ' squared errors and cross errors
    bvgarch.append @logl logl
    bvgarch.append sqres1 = (y1-mu(1)-lambda(1)*garch1)^2
    bvgarch.append sqres2 = (y2-mu(2)-lambda(2)*garch2)^2

    bvgarch.append res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)


' calculate the variance and covariance series
bvgarch.append var_y1  =  omega(1)^2 + beta(1)^2*var_y1(-1) + alpha(1)^2*sqres1(-1)
bvgarch.append var_y2  = omega(3)^2+omega(2)^2 + beta(2)^2*var_y2(-1) + alpha(2)^2*sqres2(-1)
bvgarch.append cov_y1y2 = omega(1)*omega(2) + beta(2)*beta(1)*cov_y1y2(-1) + alpha(2)*alpha(1)*res1res2(-1)

' determinant of the variance-covariance matrix
bvgarch.append deth = var_y1*var_y2 - cov_y1y2^2

' inverse elements of the variance-covariance matrix
bvgarch.append invh1 = var_y2/deth
bvgarch.append invh3 = var_y1/deth
bvgarch.append invh2 = -cov_y1y2/deth

' log-likelihood series
bvgarch.append logl =-0.5*(!mlog2pi + (invh1*sqres1+2*invh2*res1res2+invh3*sqres2) + log(deth))

' remove some of the intermediary series
' bvgarch.append @temp invh1 invh2 invh3 sqres1 sqres2 res1res2 deth


' estimate the model
smpl s1
bvgarch.ml(showopts, m=100, c=1e-5)

' change below to display different output
show bvgarch.output
graph varcov.line var_y1 var_y2 cov_y1y2
show varcov

' LR statistic for univariate versus bivariate model
scalar lr = -2*( eq1.@logl + eq2.@logl - bvgarch.@logl )
scalar lr_pval = 1 - @cchisq(lr,1)


trubador
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby trubador » Wed Dec 01, 2010 2:19 am

Lambdas are the coefficents of variances in the mean equations.

yaser
Posts: 9
Joined: Tue Nov 23, 2010 9:49 am

Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?

Postby yaser » Fri Dec 03, 2010 7:16 am

thanks for your help
I have done it with my own data set, but there is a near singular matrix error here.
Its about the EQUATION EQ2.ARCH
how can I resolve it? is there any kind of multicollinearity between regressors?


Return to “Estimation”

Who is online

Users browsing this forum: No registered users and 7 guests