Department of Economics and Business Economics

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

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    Final published version, 619 KB, PDF document

  • Christian Møller Dahl, Denmark
  • Emma M. Iglesias, Michigan State University, United States
  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages61
Publication statusPublished - 2009

    Research areas

  • Quasi-Maximum Likelihood, GARCH-M Model, Asymptotic Properties, Risk-return Relation.

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