Standard BEKK & Triangular BEKK

[econo]

Dear Friends;
I am trying to run BEKK (std) , BEKK (diag. ) models for log-return o & H index.
So I run this code in RATS 8.0 for BEKK (std):

Code: Select all

open data Y1_O_A.xls
data(format=xls,org=columns) / O A
compute gstart=2,gend=2276
garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=5,hmatrices=bekkhh, rvectors=bekkrv) gstart gend O A

I got this result :

Code: Select all

MV-GARCH, BEKK - Estimation by BFGS

Log Likelihood                     12215.6569

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(1)                       0.000283340  0.000400013      0.70833  0.47874139
2.  Mean(2)                       0.000664793  0.000280385      2.37100  0.01774018
3.  C(1,1)                        0.002027994  0.000343817      5.89846  0.00000000
4.  C(2,1)                       -0.000395421  0.000278227     -1.42122  0.15525376
5.  C(2,2)                       -0.000296307  0.000793017     -0.37365  0.70866801
6.  A(1,1)                        0.207104417  0.016768757     12.35061  0.00000000
7.  A(1,2)                       -0.045891094  0.010128710     -4.53079  0.00000588
8.  A(2,1)                        0.032267832  0.023867324      1.35197  0.17638590
9.  A(2,2)                        0.210708054  0.015582838     13.52180  0.00000000
10. B(1,1)                        0.973169654  0.004569885    212.95277  0.00000000
11. B(1,2)                        0.011234222  0.003081176      3.64608  0.00026627
12. B(2,1)                       -0.004411685  0.005757129     -0.76630  0.44349814
13. B(2,2)                        0.975466541  0.003366010    289.79906  0.00000000

Now, I have these questions and appreciate if somebody can help

1. How can I get AIC criteria?
2. how can I get conditional correlations? (to plot the graph, and export it as jpg/png ) (I know that I should use hmatrices and rvectors , so I assigned a variable to them in the models but dont know how to do next steps!)
3. in the original paper, the are using triangular BEKK , is there any trick to convert std. to triangular?
I tried to use this code( which is introduced by Mr.TOM here http://www.estima.com/forum/viewtopic.php?f=11&t=495) Then I failed! :

Code: Select all

compute n=2
dec packed vat(n,n) vbt(n,n)
dec packed vct(n,n)
dec rect   var(n,n) vbr(n,n)
compute vat=sqrt(.05)*%identity(n),vbt=sqrt(.45)*%identity(n)
compute vct=%decomp(rr)

nonlin(parmset=tbekkparms) vct vat vbt
FUNCTION %%TBEKKInit
local integer i j
compute vcs=%ltouterxx(vct)
ewise vbr(i,j)=%if(j>=i,vbt(i,j),0.0)
ewise var(i,j)=%if(j>=i,vat(i,j),0.0)
END
frml hf = vcs+%mqform(h{1},vbr)+%mqform(uu{1},var)
maximize(title="Triangular BEKK",start=%%TBEKKInit(),parmset=meanparms+tbekkparms,$
  method=bfgs,iters=400,pmethod=simplex,piters=5) logl gstart gend

because : rr is not introduced! ( actually in that code it is for initial setup parameters for MAXIMIZE code)
4.Then what is C in the table 6 first colmn.?
5.is Mean (1) the same as AR ?
6.is mean (2) the same as MA?

thanks in advance.

[TomDoan]

Dear Friends;
I am trying to run BEKK (std) , BEKK (diag. ) models for log-return oil prices & HS300 index. (bi-variate) according to table 6 of Prof. McAleer and Prof. Chang paper:
http://ideas.repec.org/p/kyo/wpaper/743.html
So I run this code in RATS 8.0 for BEKK (std):

Code: Select all

open data Y1_O_A.xls
data(format=xls,org=columns) / O A
compute gstart=2,gend=2276
garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=5,hmatrices=bekkhh, rvectors=bekkrv) gstart gend O A

I got this result :

Code: Select all

MV-GARCH, BEKK - Estimation by BFGS

Log Likelihood                     12215.6569

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(1)                       0.000283340  0.000400013      0.70833  0.47874139
2.  Mean(2)                       0.000664793  0.000280385      2.37100  0.01774018
3.  C(1,1)                        0.002027994  0.000343817      5.89846  0.00000000
4.  C(2,1)                       -0.000395421  0.000278227     -1.42122  0.15525376
5.  C(2,2)                       -0.000296307  0.000793017     -0.37365  0.70866801
6.  A(1,1)                        0.207104417  0.016768757     12.35061  0.00000000
7.  A(1,2)                       -0.045891094  0.010128710     -4.53079  0.00000588
8.  A(2,1)                        0.032267832  0.023867324      1.35197  0.17638590
9.  A(2,2)                        0.210708054  0.015582838     13.52180  0.00000000
10. B(1,1)                        0.973169654  0.004569885    212.95277  0.00000000
11. B(1,2)                        0.011234222  0.003081176      3.64608  0.00026627
12. B(2,1)                       -0.004411685  0.005757129     -0.76630  0.44349814
13. B(2,2)                        0.975466541  0.003366010    289.79906  0.00000000

Now, I have these questions and appreciate if somebody can help

1. How can I get AIC criteria?

@regcrits works for any estimation which generates a log likelihood.

2. how can I get conditional correlations? (to plot the graph, and export it as jpg/png ) (I know that I should use hmatrices and rvectors , so I assigned a variable to them in the models but dont know how to do next steps!)

set ccorr %regstart() %regend() = %cvtocorr(bekkhh)(1,2)
graph(other options)
# ccorr

You can't directly go to JPG or PNG. Use WMF or EPS to get it into another program first (though if your target can take EPS, it's generally better to do that).

3. in the original paper, the are using triangular BEKK , is there any trick to convert std. to triangular?
I tried to use this code( which is introduced by Mr.TOM here http://www.estima.com/forum/viewtopic.php?f=11&t=495) Then I failed! :

Code: Select all

compute n=2
dec packed vat(n,n) vbt(n,n)
dec packed vct(n,n)
dec rect   var(n,n) vbr(n,n)
compute vat=sqrt(.05)*%identity(n),vbt=sqrt(.45)*%identity(n)
compute vct=%decomp(rr)

nonlin(parmset=tbekkparms) vct vat vbt
FUNCTION %%TBEKKInit
local integer i j
compute vcs=%ltouterxx(vct)
ewise vbr(i,j)=%if(j>=i,vbt(i,j),0.0)
ewise var(i,j)=%if(j>=i,vat(i,j),0.0)
END
frml hf = vcs+%mqform(h{1},vbr)+%mqform(uu{1},var)
maximize(title="Triangular BEKK",start=%%TBEKKInit(),parmset=meanparms+tbekkparms,$
  method=bfgs,iters=400,pmethod=simplex,piters=5) logl gstart gend

because : rr is not introduced! ( actually in that code it is for initial setup parameters for MAXIMIZE code)

TBEKK and DBEKK were added to the GARCH instruction with 8.2. RR is defined earlier in that program. It's the covariance matrix of the original data.

4.Then what is C in the table 6 first colmn.?
5.is Mean (1) the same as AR ?
6.is mean (2) the same as MA?

You're not estimating an ARMA model for the mean, just constants. The C's would correspond to mean(1) and mean(2). Note that Table 6 in the paper is for DCC, not BEKK.

While they are using ARMA(1,1) mean models, I don't like the looks of their ARMA estimates---they show every sign of cancellation problems which means you don't need either.

[econo]

Thanks a lot for your kind response.
This code is not working as I am using version RATS 8.0

Code: Select all

graph(other options)

This is the Error :

Code: Select all

## OP3. This Instruction Does Not Have An Option OTH
>>>>graph(other <<<<

You are right. In their Table 7. (BEKK model) , They are using ARMA mean triangular (? the BOLD C matrix is triangular) BEKK.
So, How can I apply this in RATS?

[TomDoan]

"other options" means whatever options (header, footer, ...) you want.

If you want to do TBEKK with the RATS 8.0, you need to use the MAXIMIZE code that you were showing earlier. You just need to make sure you get all the setup code.

[econo]

In standard BEKK Results of this Code:

garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=5)

I can get the A,B, C matrices
Also I got mean (1) ,mean(2) coefficients.

Can somebody show me the MEAN Equation ?
is it :
y_t=μ_t+ε_t

[TomDoan]

1. Mean(1) 0.000283340 0.000400013 0.70833 0.47874139
2. Mean(2) 0.000664793 0.000280385 2.37100 0.01774018

mu for the first element of y is 0.000283340 and mu for the second is 0.000664793. The mu's aren't time-varying.

[econo]

How can I calculate n(t) from this formula?

ε_t=H_t^(1/2) η_t


Also How can I export ε_t and H_t to the CSV format?

[TomDoan]

Those are multivariate standardized residuals, as described in the User's Guide. Note that there are different sets depending upon which "square root" of H you choose.

You can use the MVHSERIES option to get the H broken into separate series for each component. Use RVECTORS and use SET instructions to break the raw residuals down. Once you have them in series, you can use COPY.

[econo]

Dear Tom;

I used this code:

Code: Select all

open data Main.xls
data(format=xls,org=columns) / O S
compute gstart=2,gend=2300
garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=5,hmatrices=bekkhh, MVHSERIES=bekkHmatrix, rvectors=bekkrv) gstart gend O S

set ccorr %regstart() %regend() = %cvtocorr(bekkhh)(1,2)
open copy x12.xls
copy(data,format=xls,org=columns)  /bekkHmatrix

open copy x11.xls
copy(data,format=xls,org=columns)  /bekkrv

Now, I think these are my variables:
1. bekkHmatrix is H(t) {variance-covariance Matrix)
2. ccorr is Conditional correlations (?? is this true? maybe it is covariance of HMATRICES not correlation? )

*the help of RATS says:
Note that HMATRICES and MVHSERIES save the same information, just in different variable types.
but as I am checking my ccorr and bekkHmatrix(2,1) are not the same!

3. bekkrv is supposed to give me residuals. (but gives me error!!- I am sure I should use SET, but couldnt figure it out !)

also whats is STDRESIDS option? what this gives me and has difference with rvectors.

Best Regards
and thank a lot in advance.

[TomDoan]

Dear Tom;

I used this code:

Code: Select all

open data Main.xls
data(format=xls,org=columns) / Opec Shenzen
compute gstart=2,gend=2354
garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=5,hmatrices=bekkhh, MVHSERIES=bekkHmatrix, rvectors=bekkrv) gstart gend Opec Shenzen

set ccorr %regstart() %regend() = %cvtocorr(bekkhh)(1,2)
open copy x12.xls
copy(data,format=xls,org=columns)  /bekkHmatrix

open copy x11.xls
copy(data,format=xls,org=columns)  /bekkrv

Now, I think these are my variables:
1. bekkHmatrix is H(t) {variance-covariance Matrix)

Correct

2. ccorr is Conditional correlations (?? is this true? maybe it is covariance of HMATRICES not correlation? )

It's the conditional correlation.

*the help of RATS says:
Note that HMATRICES and MVHSERIES save the same information, just in different variable types.
but as I am checking my ccorr and bekkHmatrix(2,1) are not the same!

One's the correlation, one the covariance so they shouldn't be the same.

3. bekkrv is supposed to give me residuals. (but gives me error!!- I am sure I should use SET, but couldnt figure it out !)

set r1 = bekkrv(t)(1)
set r2 = bekkrv(t)(2)

also whats is STDRESIDS option? what this gives me and has difference with rvectors.

That's added with version 9. It gives the standardized residuals, which are the eta's in your previous question. RVECTORS gives the unadjusted residuals which aren't really useful for any diagnostics since they are heteroscedastic.

[econo]

Dear Tom;

I used the version 9.0 so I got this error after the running this SET :

Code: Select all

set r1 = bekkrv(t)(1) 

## MAT15. Subscripts Too Large or Non-Positive
Error was evaluating entry 2355

But I got ETA series. Thanks alot

[econo]

Dear Tom;

I checked several times , the ETA is not normally distributed! it looks like normal but has skewness, so as I checked it follows Logistic distribution.
I was wondering maybe something wrong!
I really appreciate, if you can help me to access the residuals.

best regards

[TomDoan]

Dear Tom;

I checked several times , the ETA is not normally distributed! it looks like normal but has skewness, so as I checked it follows Logistic distribution.
I was wondering maybe something wrong!
I really appreciate, if you can help me to access the residuals.

best regards

First of all, the logistic isn't skewed either.

There's no reason to be concerned if the standardized residuals aren't Normal. If they have fat tails (rather than simple skewness), then you might need to use a conditional t distribution rather than the Normal. However, the estimates of the GARCH parameters are still consistent even if the residuals aren't conditionally Normal---you might need to add the ROBUSTERRORS option to correct the covariance matrix, but that's all.

[econo]

Dear Tom;

I am using Standard residuals to estimate Copula.
when I am using Univariate-garch, then finding standard residuals.using these standard residuals for estimating copula gives me reasonable results.
but ETA's from BEKK GARCH doesn't give me any reasonable results. Thats why I think something is not working right!

[TomDoan]

Dear Tom;

I am using Standard residuals to estimate Copula.
when I am using Univariate-garch, then finding standard residuals.using these standard residuals for estimating copula gives me reasonable results.
but ETA's from BEKK GARCH doesn't give me any reasonable results. Thats why I think something is not working right!

The multivariate standardized residuals from a multivariate GARCH model will be very different from a set of univariate standardized residuals. The former are designed by construction to be uncorrelated with each other---the latter would, in the typical situation, be fairly highly correlated. So the fact that the results of applying copula analysis to them produces very different results wouldn't be unexpected. The correct process for copula estimation is to do the univariate marginal models. See copula.rpf.