Estimation of time-varying high-dimensional covariance matrices

by

Anastasios Th. Plataniotis and Petros Dellaportas

Abstract

A multivariate stochastic volatility model is estimated by first applying a spectral decomposition with eigenvalues and eigenvectors changing across time, and then transforming the eigenvector matrix as a product of Givens rotation matrices. The time-varying eigenvectors and Givens angles are then assumed to follow an AR(1) process. Since interest lies in high dimensional matrices, Bayesian estimation is achieved via integrated nested Laplace approximations. The nature of our parameterisation allows for parsimonious models in which not all eigenvectors or

eigenvalues are estimated via an AR(1) process but can be considered to be constant over time. The model is illustrated with a dataset of 100 stocks.