GARCH volatility spillover

[dfschoi]

I am a new user (need encouragement). This is my first question at this forum. I want to find out if the volatility of two return series are spilling over to each other. When I was using Eviews, I added an additional volatility variable of return Y to the GARCH model of return X to see if the coefficient of the volatility of return Y is significant. In RATS, I can run the command GARCH(P=1,Q=1,METHOD=BHHH) / returnX returnY. But I do not know how to interpret the RATS results. I have been looking for such help for many years. Can someone please give me some guidance? I need to see a simple example using two variables, i.e., bivariate GARCH. Thank you!

[TomDoan]

The usual way of defining "spillover" in volatility is the inclusion of the cross terms of lagged squared residuals, not the variances. You can do that with MV=CC or MV=DCC with the VARIANCES=SPILLOVER option. (There's also the VARIANCES=VARMA option, which includes both lagged squared residuals and lagged variances). These are both included in the GARCHMV.RPF example. The output from the spillover model is:

Code: Select all

MV-GARCH, CC with Spillover Variances - Estimation by BFGS
Convergence in    77 Iterations. Final criterion was  0.0000020 <=  0.0000100
Usable Observations                      6236
Log Likelihood                    -12758.1968

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(1)                      -0.000141939  0.006521933     -0.02176  0.98263678
2.  Mean(2)                      -0.000222974  0.005988593     -0.03723  0.97029909
3.  Mean(3)                       0.006828726  0.007526142      0.90733  0.36423009
4.  C(1)                          0.017631325  0.002171319      8.12010  0.00000000
5.  C(2)                          0.027158298  0.002601285     10.44034  0.00000000
6.  C(3)                          0.031588982  0.002896877     10.90450  0.00000000
7.  A(1,1)                        0.167283354  0.012310689     13.58846  0.00000000
8.  A(1,2)                        0.016948612  0.010790888      1.57064  0.11626602
9.  A(1,3)                       -0.041555601  0.008717765     -4.76677  0.00000187
10. A(2,1)                       -0.054861994  0.007252455     -7.56461  0.00000000
11. A(2,2)                        0.162005243  0.012470818     12.99075  0.00000000
12. A(2,3)                       -0.006567204  0.008113177     -0.80945  0.41825686
13. A(3,1)                       -0.030622145  0.005235653     -5.84877  0.00000000
14. A(3,2)                       -0.006212673  0.007810006     -0.79548  0.42633662
15. A(3,3)                        0.125423712  0.007609623     16.48225  0.00000000
16. B(1)                          0.823058841  0.012234889     67.27146  0.00000000
17. B(2)                          0.815611878  0.011289314     72.24636  0.00000000
18. B(3)                          0.838647447  0.009351476     89.68076  0.00000000
19. R(2,1)                        0.571420148  0.008110372     70.45548  0.00000000
20. R(3,1)                        0.584890051  0.008252475     70.87450  0.00000000
21. R(3,2)                        0.830999830  0.003816221    217.75463  0.00000000

You can do an LR test by comparing this with just MV=CC without VARIANCES=SPILLOVER, but it seems rather clear that many of the spillover terms are significant; somewhat interestingly, though, they are mainly negative and the largest ones are cross effects between country 1 (Japan) and one of the European countries (France = 2 and Switzerland = 3). For instance, A(2,1) is the term for the effect of Japan's lagged squared residual on France's exchange rate (all these are vs the dollar).

[dfschoi]

Hi Tom, thanks for replying my first question at the Forum. Please advise me where I can find GARCHMV.RPF and the dataset so that I can run and see if I can get the same result as yours.

[TomDoan]

Hi Tom, thanks for replying my first question at the Forum. Please advise me where I can find GARCHMV.RPF and the dataset so that I can run and see if I can get the same result as yours.

It's one of the standard examples which would be in your examples and procedures folder, which is typically in My Documents\WinRATS xxx (xxx is the version information).

[dfschoi]

Hi Tom, found GARCHMV.RPF. Thank you!