Dependence Estimation for High Frequency Sampled Multivariate CARMA Models
Abstract
The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior of the cross-covariances between different components of the model. We will see that the limit distribution of the sample autocovariance function has a similar structure in the continuous-time and in the discrete-time model. As special case we consider a CARMA (one-dimensional MCARMA) process. For a CARMA process we prove Bartlett's formula for the sample autocorrelation function. Bartlett's formula has the same form in both models, only the sums in the discrete-time model are exchanged by integrals in the continuous-time model. Finally, we present limit results for multivariate MA processes as well which are not known in this generality in the multivariate setting yet.
Cite
@article{arxiv.1410.6273,
title = {Dependence Estimation for High Frequency Sampled Multivariate CARMA Models},
author = {Vicky Fasen},
journal= {arXiv preprint arXiv:1410.6273},
year = {2015}
}