Modelling the Volatility-Return Trade-off when Volatility may be Nonstationary
AbstractIn 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.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-59.
Date of creation: 02 Oct 2009
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Web page: http://www.econ.au.dk/afn/
Quasi-Maximum Likelihood; GARCH-M Model; Asymptotic Properties; Risk-return Relation.;
Other versions of this item:
- Dahl Christian M & Iglesias Emma, 2011. "Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-32, February.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-10 (All new papers)
- NEP-ECM-2010-01-10 (Econometrics)
- NEP-ETS-2010-01-10 (Econometric Time Series)
- NEP-FMK-2010-01-10 (Financial Markets)
- NEP-ORE-2010-01-10 (Operations Research)
- NEP-RMG-2010-01-10 (Risk Management)
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