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Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary

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  • Dahl Christian M

    (University of Southern Denmark)

  • Iglesias Emma

    (University of Essex)

Abstract

In this paper, a new GARCH-M type model, denoted as 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. We provide an empirical illustration showing the empirical relevance of the GARCH-AR model based on modeling a wide range of leading U.S. stock return series.

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Bibliographic Info

Article provided by De Gruyter in its journal Journal of Time Series Econometrics.

Volume (Year): 3 (2011)
Issue (Month): 1 (February)
Pages: 1-32

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Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:1:n:10

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