Extended Yule-Walker Identification of a VARMA Model Using Single- or Mixed-Frequency Data

• Activity Number: 593
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Peter Zadrozny*+
• Companies: Bureau of Labor Statistics
• Keywords: nonlinear estimation ; state-space representation ; matrix polynomials

Abstract

Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for estimating a vector autogressional (VAR) model using mixed-frequency data and illustrated its accuracy relative to MEL. The present paper extends XYW to estimate also MA parameters of a VARMA model using mixed-frequency data and proves that the estimates are consistent. The extension has three steps. Step 1 estimates the AR parameters consistently by solving a linear system of equations. Given the estimated AR parameters, Step 2 solves another linear system of equations based on forward YW equations for coefficients of a spectral representation of the MA term. Step 3 factors the spectral representation to yield a consistent estimate of an invertible representation of the MA term. Although Step 3 is nonlinear, it can be implemented reliably, accurately, and quickly using an eigenvalue method for solving linear rational expectations models, which, unlike MLE, does not require starting values.