A Stationary Parameterization of Var and Varma Models

• Activity Number: 324
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Peter Linton*+ and Anindya Roy and Tucker Sprague McElroy
• Companies: University of Maryland Baltimore County and University of Maryland Baltimore County and U.S. Census Bureau
• Keywords: Multivariate Time Series ; Bayesian ; VAR ; VARMA ; Econometrics

Abstract

We present a convenient re-parameterization of a vector autoregressive (VAR) model that allows the use of unconstrained estimation methods for the new parameters, while maintaining the constraint of stationarity under the original parameters. Applications include unconstrained optimization of the VAR(p) Gaussian likelihood, as well as elicitation of priors that are compactly supported upon the stable parameter set. Although the VAR setting has Yule-Walker fitting methods, there are no such methods for the VARMA setting. We empirically compare results from both frequentist and bayesian fitting methods. There is great advantage to the Bayesian methodology, as the priors on transformed parameters naturally induce a stationary posterior distribution for the non-transformed model parameters, which can be a difficult posterior to sample from without projection methods. Results are extendable to invertible VMA(q) processes and VARMA(p,q) processes.