Modelling the Volatility-Return Trade-off when Volatility may be Nonstationary

Christian Dahl and Emma Iglesias

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: In this paper a new GARCH–M type model, denoted the GARCH-AR, is proposed. In particular, it is shown that it is possible to generate a volatility-return trade-off in a regression model simply by introducing dynamics in the standardized disturbance process. Importantly, the volatility in the GARCH-AR model enters the return function in terms of relative volatility, implying that the risk term can be stationary even if the volatility process is nonstationary. We provide a complete characterization of the stationarity properties of the GARCH-AR process by generalizing the results of Bougerol and Picard (1992b). Furthermore, allowing for nonstationary volatility, the asymptotic properties of the estimated parameters by quasi-maximum likelihood in the GARCH-AR process are established. Finally, we stress the importance of being able to choose correctly between AR-GARCH and GARCH-AR processes: First, it is shown, by a small simulation study, that the estimators for the parameters in an ARGARCH model will be seriously inconsistent if the data generating process actually is a GARCH-AR process. Second, we provide an LM test for neglected GARCH-AR effects and discuss its finite sample size properties. Third, we provide an empirical illustration showing the empirical relevance of the GARCH-AR model based on modelling a wide range of leading US stock return series.

Keywords: Quasi-Maximum Likelihood; GARCH-M Model; Asymptotic Properties; Risk-return Relation. (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 G12 (search for similar items in EconPapers)
Pages: 61
Date: 2009-10-02
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-fmk, nep-ore and nep-rmg
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Citations: View citations in EconPapers (1)

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Journal Article: Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2009-59

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