Modelling time-varying conditional correlations in the volatility of Tapis oil spot and forward returns

Abstract

This paper estimates the dynamic conditional correlations in the returns on Tapis oil spot and one-month forward prices for the period 2 June 1992 to 16 January 2004, using recently developed multivariate conditional volatility models, namely the Constant Conditional Correlation Multivariate GARCH (CCC–MGARCH) model of Bollerslev (1990 Bollerslev, T. 1990. Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH approach. Review of Economics and Statistics, 72: 498–505. [Crossref], [Web of Science ®] , [Google Scholar]), Vector Autoregressive Moving Average–GARCH (VARMA–GARCH) model of Ling and McAleer (2003 Ling, S and McAleer, M. 2003. Asymptotic theory for a vector ARMA–GARCH model. Econometric Theory, 19: 278–308. [Crossref] , [Google Scholar]), VARMA–Asymmetric GARCH (VARMA–AGARCH) model of Hoti et al. (2002 Hoti, S, Chan, F and McAleer, M. Structure and asymptotic theory for multivariate asymmetric volatility: empirical evidence for country risk ratings. July2002, Brisbane, Australia. Paper presented to the 2002 Australasian Meeting of the Econometric Society, [Google Scholar]), and the Dynamic Conditional Correlation (DCC) model of Engle (2002 Engle, RF. 2002. Dynamic conditional correlation: a new simple class of multivariate GARCH models. Journal of Business and Economic Statistics, 20: 339–50. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The dynamic correlations are extremely useful in determining whether the spot and forward returns are substitutes or complements, which can be used to hedge against contingencies. Both the univariate ARCH and GARCH estimates are significant for spot and forward returns, whereas the estimates of the asymmetric effect at the univariate level are not statistically significant for either spot or forward returns. Standard diagnostic tests show that the AR(1)–GARCH(1, 1) and AR(1)–GJR(1, 1) specifications are statistically adequate for both the conditional mean and the conditional variance. The multivariate estimates for the VAR(1)–GARCH(1, 1) and VAR(1)–AGARCH(1, 1) models show that the ARCH and GARCH effects for spot (forward) returns are significant in the conditional volatility model for spot (forward) returns. Moreover, there are significant interdependences in the conditional volatilities between the spot and forward markets. The multivariate asymmetric effects are significant for both spot and forward returns. Overall the multivariate VAR(1)–AGARCH(1, 1) dominates its symmetric counterpart. The calculated constant conditional correlations between the conditional volatilities of spot and forward returns using CCC–GARCH(1, 1), VAR(1)–GARCH(1, 1) and VAR(1)–AGARCH(1, 1) are very close to 0.93. Virtually identical results are obtained when the three constant conditional correlation models are extended to include two lags in both the ARCH and GARCH components. Finally, the estimates of the two DCC parameters are statistically significant, which makes it clear that the assumption of constant conditional correlation is not supported empirically. This is highlighted by the dynamic conditional correlations between spot and forward returns, for which its sample mean is virtually identical to the computed constant conditional correlation, regardless of whether a DCC–GARCH(1, 1) or a DCC–GARCH(2, 2) is used. For these models, the dynamic conditional correlations are in the range (0.417, 0.993) and (0.446, 0.993), signifying medium to extreme interdependence. Therefore, the dynamic volatilities in the returns in Tapis oil spot and forward markets are generally interdependent over time. These findings suggest that a sensible hedging strategy would consider spot and forward markets as being characterized by different degrees of substitutability.