Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations

Authors:
Peter J. Brockwell;Eckhard Schlemm
Affiliations:
Department of Statistics, Colorado State University, USA and Department of Statistics, Columbia University, USA;TUM Institute for Advanced Study & Fakultäät für Mathematik, Technische Universität München, Germany
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 2
Cited 0

Multivariate fractionally integrated CARMA processes

Journal of Multivariate Analysis
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)

Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the parametric estimation of the driving Levy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0,h,2h,...). Beginning with a new state space representation, we develop a method to recover the driving Levy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving Levy process from discrete-time observations of the MCARMA process. We show that, if the sampling interval h=h"N is chosen dependent on N, the length of the observation horizon, such that Nh"N converges to zero as N tends to infinity, then any suitable generalized method of moments estimator based on this reconstructed sample of unit increments has the same asymptotic distribution as the one based on the true increments, and is, in particular, asymptotically normally distributed.