Inference for Lévy-Driven, Continuous-Time ARMA Processes

• Activity Number: 79
• Type: Invited
• Date/Time: Monday, August 4, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economics Statistics Section
• Author(s): Richard A. Davis*+ and Peter J. Brockwell and Yu Yang
• Companies: Columbia University and Colorado State University and Colorado State University

Abstract

Continuous-time ARMA (CARMA) processes with non-negative kernel and driven by non-decreasing Lévy processes constitute a very general class of stationary, non-negative continuous-time processes. In financial econometrics, for example, they have been used to model stochastic volatility (e.g., Barndorff-Nielsen and Shephard (2001) and Todorov and Tauchen (2006)). In this paper, we develop a highly efficient method of estimation for the coefficients of such models, taking advantage of the non-negativity of the driving process. We also show how to reconstruct the background driving Lévy process from a continuously observed realization of the CARMA process and use this result to estimate the increments of the Lévy process itself when closely spaced observations are available.