Estimation of VARMA Models

Abstract

In this chapter, maximum likelihood estimation of the coefficients of a VARMA model is considered. Before we can proceed to the actual estimation, a unique set of parameters must be specified. In this context, the problem of nonuniqueness of a VARMA representation becomes important. This identification problem, that is, the problem of identifying a unique structure among many equivalent ones, is treated in Section 12.1. In Section 12.2, the Gaussian likelihood function of a VARMA model is considered. A numerical algorithm for maximizing it and, thus, for computing the actual estimates is discussed in Section 12.3. The asymptotic properties of the ML estimators are the subject of Section 12.4. Forecasting with estimated processes and impulse response analysis are dealt with in Sections 12.5 and 12.6, respectively.