A1008
Title: Likelihood asymptotics for stationary Gaussian arrays
Authors: Fabian Mies - Delft University of Technology (Netherlands) [presenting]
Carsten Chong - HKUST (Hong Kong)
Abstract: Arrays of stationary Gaussian time series can arise naturally in econometric applications, e.g., the discretization of continuous-time stochastic processes, or be introduced artificially to model persistence via so-called local-to-unity models, i.e., linear time series models with parameters close to a unit root. For the parametric statistical estimation of these stationary models, the spectral density plays a central role. In particular, classical results in time series analysis suggest that the Gaussian likelihood and Fisher information may be approximated in terms of the spectral density, and conditions for the efficiency of the MLE have been formulated in the literature. Unfortunately, these general results do not cover arrays of time series. The contribution is to show in which way the asymptotic likelihood theory needs to be adapted for the array case and to demonstrate that this yields a straightforward approach to studying a broad class of processes. As a motivating example, the mixed fractional Brownian motion estimation is investigated based on high-frequency observations. Findings reveal that the achievable convergence rates depend intricately on the size of the various components and their intertemporal and cross-temporal dependence structure.
