This finding of significant volatility transmission across series in the multivariate GARCH context may be caused by a common volatility shift across the two series. We conclude that researchers should detect endogenous volatility breaks and incorporate these breaks into the estimation model to obtain an accurate estimate of the volatility transmission dynamics across series over time. It also results in a true hedge ratio of zero, regardless of the presence of structural breaks in volatility.
We used different GARCH parameters and unconditional variance levels in the first five cases (P1 to P5) in the two series. Consequently, in the second case, a break is induced in the two variables, but the break size is different. Our simulated series have no volatility spillovers, but we may have introduced structural breaks in the unconditional variance levels.
In the BEKK case, testing for the absence of variance spillover may require a comparison of the cases where the set of tested parameters includes the intercept 𝑐12. Furthermore, in the case of a data-generating process with nonzero correlation, the dynamics of the conditional covariance can be the source of spurious spillover effects. Panel D of Table 3 shows that introducing correlation between the innovations in the data generation process leads to a clear worsening of rejection rates.
The two quantiles of estimated hedge ratios in Table 6 show that there is a significant increase in the variability of the hedge ratios in the simulations when we have a break.
Empirical Results
If the hedge ratios are large, the hedge performance of using that estimated hedge ratio is not as good compared to an unconditional (constant) hedge ratio (see Fan, Li and Park, 2016; Lien, 2010). Some breaks are very close together in series, while others are far apart. Even if the breaks are caused by a common event in different markets, we still expect a different impact on volatility in different markets, as the speed of information flows between markets is different, as suggested by Ross (1989).
We then estimate the BEKK model as given in Equation 11 and report the results in Table 9 (Panel A). We find that all four coefficient terms of the news and volatility spillover (e.g. how h22 affects h11) are significant at 1%. Finally, we estimate the same BEKK model from above, but consider the fractions with dummy variables.
Di is a 22 square diagonal matrix of parameters, and Xi is a 12 row vector of break control variables, and n is the number of break points found in variance. If the first series undergoes a volatility breakout at time t, then the first element will take a value of zero before time t and a value of one from time t onwards. The estimation results from the model, which incorporates breaks, are reported in Table 9 (Panel B).17 We find that all four coefficient terms controlling if news and volatility.
17 As Table 9 shows, the log-likelihood increased after accounting for structural breaks, indicating that the model with structural breaks fits better. The likelihood ratio statistic is calculated as 2[L(Θ1)-L(Θ0)] where L(Θ1) and L(Θ0) are the maximum log-likelihood values obtained from the GARCH models with and without structural breaks, respectively . This statistic is asymptotically distributed as χ2 with degrees of freedom equal to the number of restrictions from the more general model (with breaks) to the more parsimonious model (without breaks).
Basically, the results show that there is no significant transmission of shocks and volatility between the two series after accounting for the discontinuities. The average estimated hedge ratio is 0.70 over the entire sample period, which has changed significantly from the previous value of 0.48. Thus, the empirical evidence reported here is consistent with our overall conclusion drawn from our simulations that structural breaks cause spurious volatility transmission and estimated hedge ratios are substantially affected by these structural breaks.
Conclusion
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This table reports the rejection frequencies of the Wald test for testing the null hypothesis of zero coefficients in the off-diagonal terms of the parameter matrices A, B and C (with and without intercept) of the BEKK model Ht1C'C B'HtBA't t'A at the 1% level of significance. Specifically, this table reports the rejection frequencies of the Wald test for testing the null hypothesis of zero coefficients in the off-diagonal terms of the parameter matrices A, B, and C (with and without an intercept) of the BEKK model Ht1C 'CB'HtBA' tt'A at 1% level of significance. Specifically, this table reports the rejection frequencies of the Wald test for testing the null hypothesis of zero coefficients in the off-diagonal terms of the parameter matrices A, B, and C (with and without an intercept) of the BEKK model.
Notes: This table reports the frequency of the 1% statistically significant individual parameters of the BEKK model given as. We see that the frequency of 1% statistically significant coefficient goes to 0.01 to increase the size of the sample in the case of off-diagonal coefficients (12 and 21).
