Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias
53 Pages Posted: 16 Mar 2008
There are 2 versions of this paper
Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias
Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias
Date Written: February 2008
Abstract
It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics of the aggregate volatility involves additional lags that reflect the moments of the distribution of the individual persistence parameters. Then the paper describes a consistent estimator of the aggregate process, based on nonlinear least squares. A simulation study reveals that this aggregation-corrected estimator performs very well under realistic sets of parameters. Last, this approach is extended to a multi-sector context. This extension is used to evaluate the importance of the aggregation bias. Using size and book-to-market portfolios, I show that the investor is willing to pay one fifth of her expected return to switch from the standard GARCH(1,1) estimator to the aggregation-corrected estimator.
Keywords: Contemporaneous aggregation, Heterogeneity, Volatility, GARCH model
JEL Classification: C13, C21, G11
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Modeling and Forecasting Realized Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
Modeling and Forecasting Realized Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Realized Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Stock Return Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
By Torben G. Andersen, Tim Bollerslev, ...
-
Range-Based Estimation of Stochastic Volatility Models
By Sassan Alizadeh, Michael W. Brandt, ...
-
By Torben G. Andersen, Tim Bollerslev, ...
-
By Torben G. Andersen, Tim Bollerslev, ...