A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics

Manabu Asai and Michael McAleer

No 16-065/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA-GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature.

Keywords: Multivariate conditional volatility; Vector random coefficient autoregressive process; Asymmetry; Long memory; Exogenous variables; Dynamic conditional correlations; Regularity conditions; Asymptotic properties (search for similar items in EconPapers)
JEL-codes: C22 C52 C58 G32 (search for similar items in EconPapers)
Date: 2016-08-29
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Working Paper: A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20160065

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