Flexible Spectral Models for Multivariate Time Series

• Activity Number: 160
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Scott Holan*+ and Tucker McElroy
• Companies: University of Missouri and U.S. Census Bureau
• Keywords: Bayesian ; Econometrics ; Multivariate ; Spectral density matrix

Abstract

Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to work with a stable, or at least stationary, representation. To fit such models, one must impose restrictions on the coefficient matrices to ensure that certain determinants are nonzero; which, except in special cases, may prove burdensome. To circumvent these difficulties, we propose a flexible frequency domain model in terms of the spectral density matrix. The model specification we provide naturally guarantees that the spectral density matrix is always positive definite at all frequencies and is readily formulated with an unrestricted parameter space on the model coefficients. Moreover, our approach leads to a stable, and thus stationary representation. To make the model viable we provide explicit formulas that allow rapid computation of the autocovariance matrix and discuss matters of co-integration. We illustrate the utility of our approach through a Bayesian analysis of macroeconomic time series.