User: Guest  Login
Document type:
Zeitschriftenaufsatz 
Author(s):
Brockwell, P. J., and Schlemm, E. 
Title:
Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations 
Abstract:
We consider the parametric estimation of the driving Lévy 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 Lévy 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 Lévy process from discrete-time observations of the MCARMA process. We show that, if the sampling interval h = hN is chosen dependent on N, the length of the observation horizon, such that NhN 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. 
Journal title:
Journal of Multivariate Analysis 
Year:
2013 
Journal volume:
115 
Pages contribution:
217–251 
Reviewed:
ja 
Language:
en 
Status:
Preprint / submitted 
Semester:
SS 11 
TUM Institution:
Lehrstuhl für Mathematische Statistik 
Format:
Text