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Fractional Integration and Fat Tails for Realized Covariance Kernels and Returns

Andre Lucas () and Anne Opschoor
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Anne Opschoor: VU University Amsterdam, the Netherlands

No 16-069/IV, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We introduce a new fractionally integrated model for covariance matrix dynamics based on the long-memory behavior of daily realized covariance matrix kernels and daily return observations. We account for fat tails in both types of data by appropriate distributional assumptions. The covariance matrix dynamics are formulated as a numerically efficient matrix recursion that ensures positive definiteness under simple parameter constraints. Using intraday stock data over the period 2001-2012, we construct realized covariance kernels and show that the new fractionally integrated model statistically and conomically outperforms recent alternatives such as the Multivariate HEAVY model and the multivariate HAR model. In addition, the long-memory behavior is more important during non-crisis periods.

Keywords: multivariate volatility; fractional integration; realized covariance matrices; heavy tails; matrix-F distribution; score dynamics (search for similar items in EconPapers)
JEL-codes: C32 C58 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2016-09-02, Revised 2017-07-07
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