Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

ABSTRACT

We propose a state-space approach for GARCH models with time-varying parameters able to deal with non-stationarity that is usually observed in a wide variety of time series. The parameters of the non-stationary model are allowed to vary smoothly over time through non-negative deterministic functions. We implement the estimation of the time-varying parameters in the time domain through Kalman filter recursive equations, finding a state-space representation of a class of time-varying GARCH models. We provide prediction intervals for time-varying GARCH models and, additionally, we propose a simple methodology for handling missing values. Finally, the proposed methodology is applied to the Chilean Stock Market (IPSA) and to the American Standard&Poor's 500 index (S&P500).

KEYWORDS:

• GARCH models
• local stationarity
• long-range dependence
• state-space representation
• time-varying models

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Francisco J. Rodríguez-Cortés http://orcid.org/0000-0002-2152-8619

Additional information

Funding

This work was supported by Spanish Ministry of Economy and Competitiveness [MTM2013-43917-P], Formation of Advanced Human Capital Program, Post-doctoral scholarships abroad, Conicyt, Chile [Folio 74150023] and University of Concepción [DIUC 215.014.024-1.0].