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

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Matteo Manera
Michael McAleer
Margherita Grasso

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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), Vector Autoregressive Moving Average--GARCH (VARMA--GARCH) model of Ling and McAleer (2003), VARMA--Asymmetric GARCH (VARMA--AGARCH) model of Hoti et al . (2002), and the Dynamic Conditional Correlation (DCC) model of Engle (2002). 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.

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Article provided by Taylor and Francis Journals in its journal Applied Financial Economics.

Volume (Year): 16 (2006)
Issue (Month): 7 (April)
Pages: 525-533
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Handle: RePEc:taf:apfiec:v:16:y:2006:i:7:p:525-533

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August. [Downloadable!] (restricted)
  2. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June. [Downloadable!]
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  3. Suhejla Hoti & Felix Chan & Michael McAleer, 2003. "Structure and Asymptotic Theory for Multivariate Asymmetric Volatility: Empirical Evidence for Country Risk Ratings," CIRJE F-Series CIRJE-F-203, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  4. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April. [Downloadable!]
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  5. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1554-1583, December. [Downloadable!]
  6. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August. [Downloadable!] (restricted)
  7. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January. [Downloadable!] (restricted)
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  8. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Jian Yang & Titus O. Awokuse, 2003. "Asset storability and hedging effectiveness in commodity futures markets," Applied Economics Letters, Taylor and Francis Journals, vol. 10(8), pages 487-491, June. [Downloadable!] (restricted)
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  10. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February. [Downloadable!]
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  12. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December. [Downloadable!] (restricted)
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  1. Vargas, Gregorio A., 2008. "What Drives the Dynamic Conditional Correlation of Foreign Exchange and Equity Returns?," MPRA Paper 7174, University Library of Munich, Germany. [Downloadable!]
  2. Chia-Lin Chang & Michael McAleer & Roengchai Tansuchat, 2009. "Modelling Conditional Correlations for Risk Diversification in Crude Oil Markets," CIRJE F-Series CIRJE-F-640, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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