CC MVEGARCH with spillovers

[Evans_felipe]

Dear Tom,
I am trying to perform a CC-MVEGARCH as CHAKER ALOUI did on "Price and volatility spillovers between exchange rates and stock indexes for the pre- and post-euro period" which defines the conditional variance equations as follows:


I am trying to get the same amount of parameters as he did, which are:


So far, i have performed a CC-MVEGARCH as follows:

Code: Select all

cal(d) 2009:1:2
open data series.xls
data(format=xls,org=columns) / BRASIL_STOCK BRASIL_EXCHANGE
*SOURCE C:\RATS\DFUNIT,SRC
*SOURCE C:\RATS\ADTEST,SRC
*DEL 1 AL 1008
compute gstart=2009:1:2,gend=2013:12:30
set brasil_rt = 100*log(BRASIL_STOCK/BRASIL_STOCK{1})
set brasil_st = 100*log(BRASIL_EXCHANGE/BRASIL_EXCHANGE{1})

system(model=var1)
variables brasil_rt brasil_st
lags 1 2
det constant
end(system)
estimate(noprint)
garch(p=2,q=1,model=var1,mv=cc,pmethod=bhhh,variance=spillover,asymmetric,piters=10,hmatrices=H,RVECTORS=U)

set z1 %regstart() %regend() = U(t)(1)/sqrt(H(t)(1,1))
set z2 %regstart() %regend() = U(t)(2)/sqrt(H(t)(2,2))
@bdindtests(number=20) z1
@bdindtests(number=20) z2

And i get the coefficient terms: C(1) C(2) A(1,1) A(1,2) A(2,1) A(2,2) B{1}(1) B{1}(2) B{2}(1) B{2}(2) D(1) D(2) R(2,1). I know that C terms are for constants, A(1,1) and (2,2) terms measures the arch effect, A(1,2) and A(2,1) measures the spillovers, B terms represent the GARCH(-1) GARCH(-2) for each equation and, R(2,1) denotes the correlation, what i don't get is:

1) The D(1) and D(2) terms... i know they are set for asymmetry effect" but as shown on my base model which parameters are they? theta(1,1) theta(1,2) theta(2,1) theta(2,2) any of them? and if they are not, how can i estimate them?

2) In this paper the volatility persistent is sum_{j=1}^P_{s} and they get a t-statistic with robust standard errors for this sum, how can i do it? and last:

3) Since i have found that these variables (brasil_rt and brasil_st) are cointegrated, how can i modify the mean equation to allow ECM??

Thanks you so much in advice,
Felipe Evans.

[TomDoan]

And i get the coefficient terms: C(1) C(2) A(1,1) A(1,2) A(2,1) A(2,2) B{1}(1) B{1}(2) B{2}(1) B{2}(2) D(1) D(2) R(2,1). I know that C terms are for constants, A(1,1) and (2,2) terms measures the arch effect, A(1,2) and A(2,1) measures the spillovers, B terms represent the GARCH(-1) GARCH(-2) for each equation and, R(2,1) denotes the correlation, what i don't get is:

1) The D(1) and D(2) terms... i know they are set for asymmetry effect" but as shown on my base model which parameters are they? theta(1,1) theta(1,2) theta(2,1) theta(2,2) any of them? and if they are not, how can i estimate them?

First, VARIANCES=SPILLOVER isn't an "E-GARCH" representation. The closest thing in the GARCH instruction to what you are doing is VARIANCES=KOUTMOS, which is a restricted version of the model from the paper---in the Koutmos model, each series has an "asymmetry index" which uses a single series-specific weighted average of the (standardized) absolute value and level which appears in both the variance and spillover terms. VARIANCES=SPILLOVER only has asymmetry terms on the "own" lagged residuals. A model with a complete set of asymmetric cross terms tends to be hard to interpret (in the model you give, there are two "spillover" coefficients in each equation, rather than one), which is why those models (and VARIANCES=VARMA) restrict the form of the asymmetry.

2) In this paper the volatility persistent is sum_{j=1}^P_{s} and they get a t-statistic with robust standard errors for this sum, how can i do it? and last:

You would do ROBUSTERRORS to get the robust (QMLE) covariance matrix. You can then use SUMMARIZE to compute the sum of the coefficients and their standard errors.

3) Since i have found that these variables (brasil_rt and brasil_st) are cointegrated, how can i modify the mean equation to allow ECM??

Your return series are cointegrated? That seems rather odd. Do they even have unit roots?

[Evans_felipe]

Thanks you Tom for you reply, i have considered what you said about VARIANCES=SPILLOVERS and i changed my model to Koutmo's (i searched for koutmos papers and its quite similar to what i am trying to do so i will keep it) and here is the code:

Code: Select all

cal(d) 2003:1:2
open data brasil.xls

data(format=xls,org=columns) / BRASIL BRASIL_REAL

SOURCE C:\RATS\BDINDTESTS.SRC
SOURCE C:\RATS\KOLMTEST.SRC
compute gstart=2003:1:2,gend=2013:12:30

compute n=2
*
* Define the return series
*
dec vect[series] y(n)
set y(1) = 100*log(BRASIL/BRASIL{1})
set y(2) = 100*log(BRASIL_REAL/BRASIL_REAL{1})

system(model=var1)
variables y(1) y(2)
lags 1 2
det constant
end(system)
estimate(noprint)

GARCH(P=2,Q=1,model=var1,MV=CC,VARIANCES=KOUTMOS,ASYMMETRIC,METHOD=BHHH,ITERS=2000,robust,rvectors=U,hmatrices=H)

set z1 %regstart() %regend() = U(t)(1)/sqrt(H(t)(1,1))
set z2 %regstart() %regend() = U(t)(2)/sqrt(H(t)(2,2))
@bdindtests(number=20) z1
@bdindtests(number=20) z2
@kolmtest(mean=0, std=1, signif=0.05,dg=36) z1
@kolmtest(mean=0, std=1, signif=0.05,dg=36) z2

I added the "robust" option to get the robust (QMLE) covariance matrix and i have tried to use summarize in many ways but it seems impossible to do with the garch wizard, would you provide me an example of how to use the summarize with garchs models?

and last; the series were not cointegrated, i did the test with the stationary series (my bad) and now i did with the I(1) one's and there is not

Thanks you very much in advice,
Felipe

[TomDoan]

You should have output that looks something like this (this was done with random data, so the coefficients are junk, but it has the same set of coefficients)

Code: Select all

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
Mean Model(Y(1))
1.  Y(1){1}                            0.0108       0.0305      0.35613  0.72174083
2.  Y(1){2}                           -0.0415       0.0327     -1.26823  0.20471671
3.  Y(2){1}                           -0.0102       0.0311     -0.32742  0.74335224
4.  Y(2){2}                            0.0022       0.0322      0.06902  0.94497336
5.  Constant                          -0.0119       0.0319     -0.37395  0.70844151
Mean Model(Y(2))
6.  Y(1){1}                            0.0251       0.0334      0.75295  0.45147871
7.  Y(1){2}                           -0.0691       0.0318     -2.16968  0.03003115
8.  Y(2){1}                            0.0161       0.0337      0.47866  0.63217800
9.  Y(2){2}                           -0.0028       0.0333     -0.08309  0.93377875
10. Constant                           0.0258       0.0328      0.78711  0.43121945

11. C(1)                               0.0062       0.0043      1.45418  0.14589708
12. C(2)                              -0.0047       0.1424     -0.03292  0.97373449
13. A(1,1)                            -0.0088       0.0043     -2.01852  0.04353699
14. A(1,2)                             0.0466       0.0311      1.50093  0.13337465
15. A(2,1)                             0.0000       0.0021      0.00227  0.99818865
16. A(2,2)                            -0.0000       0.0057     -0.00227  0.99818651
17. B{1}(1)                            1.9596       0.0074    263.43671  0.00000000
18. B{1}(2)                           -1.0747       0.0363    -29.61030  0.00000000
19. B{2}(1)                           -0.9944       0.0070   -141.22485  0.00000000
20. B{2}(2)                           -0.9514       0.0421    -22.60700  0.00000000
21. D(1)                               0.0017       0.1646      0.01040  0.99170438
22. D(2)                            -607.5121  267369.2236     -0.00227  0.99818706
23. R(2,1)                             0.0770       0.0327      2.35089  0.01872857

You want the sum of coefficients 17 and 18 and the sum of coefficients 19 and 20. You would do that with

summarize %beta(17)+%beta(18)
summarize %beta(19)+%beta(20)