This article develops a new bivariate Markov regime switching BEKK-Generalized Autoregressive Conditional Heteroscedasticity (GARCH) (RS-BEKK-GARCH) model. The model is a state-dependent bivariate BEKK-GARCH model and an extension of Gray's univariate generalized regime-switching (GRS) model to the bivariate case. To solve the path-dependency problem inherent in the bivariate regime switching BEKK-GARCH model, we propose a recombining method for the covariance term in the conditional variance-covariance matrix. The model is applied to estimate time-varying minimum variance hedge ratios for corn and nickel spot and futures prices. Out-of-sample point estimates of hedging portfolio variance show that compared to the state-independent BEKK-GARCH model, the RS-BEKK-GARCH model improves out-of-sample hedging effectiveness for both corn and nickel data. We perform White's (2000) data-snooping reality check to test for predictive superiority of RS-BEKK-GARCH over the benchmark model and find that the difference in variance reduction between BEKK-GARCH and RS-BEKK-GARCH is not statistically significant for either data set at conventional confidence levels.

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The authors develop a Markov regime-switching time-varying correlation generalized autoregressive conditional heteroscedasticity (RS-TVC GARCH) model for estimating optimal hedge ratios. The RS-TVC nests within it both the time-varying correlation GARCH (TVC) and the constant correlation GARCH (CC). Point estimates based on the Nikkei 225 and the Hang Seng index futures data show that the RS-TVC outperforms the CC and the TVC both in-and out-of-sample in terms of variance reduction. Based on H. White's (2000) reality check, the null hypothesis of no improvement of the RS-TVC over the TVC is rejected for the Nikkei 225 index contract but is not rejected for the Hang Seng index contract.

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The random coefficient autoregressive Markov regime switching model (RCARRS) for estimating optimal hedge ratios, which generalizes the random coefficient autoregressive (RCAR) and Markov regime switching (MRS) models, is introduced. RCARRS, RCAR, MRS, BEKK-GARCH, CC-GARCH, and OLS are compared with the use of aluminum and lead futures data. RCARRS outperforms all models out-of-sample for lead and is second only to BEKK-GARCH for aluminum in terms of variancereduction point estimates. White's data-snooping reality check null hypothesis of no superiority is rejected for BEKK-GARCH and RCARRS for aluminum, but not for lead.