Stability Conditions for Heteroscedastic Factor Models with Conditionally Autoregressive Betas

16 Pages Posted: 9 Aug 2011

See all articles by George A. Christodoulakis

George A. Christodoulakis

Manchester Business School

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Date Written: September 2011

Abstract

We characterize the stability properties of a heteroscedastic multi‐factor model of financial asset returns, with conditionally known factors and beta coefficients driven by general conditionally autoregressive processes. These processes generalize existing structures and address a number of empirical issues of current concern. Our analysis derives closed‐form sufficient conditions for the existence of strict stationary solutions for the composite asset conditional variances and covariances, not known previously in the literature. It is shown that stability is guaranteed when individual‐process and cross‐process restrictions hold simultaneously. Our results are also applicable to the study of the co‐movement between volatility and beta coefficients as well as between beta coefficients themselves.

Keywords: Beta coefficient, evolution, factor models, forecasting, persistence, pricing, stability, stationarity, C32, C51, C53, C58, G12, G17

Suggested Citation

Christodoulakis, George A. and Satchell, Stephen E., Stability Conditions for Heteroscedastic Factor Models with Conditionally Autoregressive Betas (September 2011). Journal of Time Series Analysis, Vol. 32, Issue 5, pp. 482-497, 2011. Available at SSRN: https://ssrn.com/abstract=1907035 or http://dx.doi.org/10.1111/j.1467-9892.2010.00706.x

George A. Christodoulakis

Manchester Business School ( email )

Crawford House
Oxford Road
Manchester, Lancashire M15 6PB
United Kingdom
00447954487777 (Phone)

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

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