School Seminars and Colloquia

Estimation for Non-negative Levy-driven CARMA Processes

Stochastic Processes and Financial Mathematics

by Peter Brockwell

Institution: Colorado State University and The University of Melbourne
Date: Thu 15th October 2009
Time: 3:15 PM
Location: Old Geology Theatre 2, The University of Melbourne

Abstract: Continuous-time autoregressive moving average (CARMA) processes with a non-negative kernel and driven by a non-decreasing Levy process constitute a useful and very general class of stationary, non-negative continuous-time processes which have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis and Yang (J. Appl. Prob., 2007) derived efficient estimates of the parameters of a non-negative Levy-driven CAR(1) (or stationary Ornstein-Uhlenbeck) process and showed how the realization of the underlying Levy process can be estimated from closely-spaced observations of the process itself. In this paper we show how the ideas of that paper can be generalized to higher order CARMA processes with non-negative kernel, the key idea being the decomposition of the CARMA process into a sum of dependent Ornstein-Uhlenbeck processes. (Joint work with Richard Davis and Yu Yang.)

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