Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary
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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.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Article
- Periodicity, Non-stationarity, and Forecasting of Economic and Financial Time Series: Editors' Introduction
- Consideration of Trends in Time Series
- Detecting Common Dynamics in Transitory Components
- Nonparametric Tests for Periodic Integration
- Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots
- Econometric Modelling of Time Series with Outlying Observations
- Forecasting Annual Inflation with Seasonal Monthly Data: Using Levels versus Logs of the Underlying Price Index
- Evaluating Automatic Model Selection
- On a Graphical Technique for Evaluating Some Rational Expectations Models
- Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary
- HYBRID GARCH Models and Intra-Daily Return Periodicity
Articles in the same Issue
- Article
- Periodicity, Non-stationarity, and Forecasting of Economic and Financial Time Series: Editors' Introduction
- Consideration of Trends in Time Series
- Detecting Common Dynamics in Transitory Components
- Nonparametric Tests for Periodic Integration
- Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots
- Econometric Modelling of Time Series with Outlying Observations
- Forecasting Annual Inflation with Seasonal Monthly Data: Using Levels versus Logs of the Underlying Price Index
- Evaluating Automatic Model Selection
- On a Graphical Technique for Evaluating Some Rational Expectations Models
- Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary
- HYBRID GARCH Models and Intra-Daily Return Periodicity
