Asymptotic Distribution for Conditional MLE of VARMA

0.1 Asymptotic Distribution for Conditional MLE of VARMA Models For a well-defined stationary and invertible VARMA(p, q) model, we assume that the innovations {at} satisfies (a) E(at|Ft−1) = 0, (b) E(atat|Ft−1) = Σ > 0, and (c) at has finite fourth moments, where Ft−1 denotes the σ-field generated by {zt−1, zt−2, · · ·}. It has been proven (Dunsmuir and Hannan, 1976, and Hannan and Deistler, 1988, and Reinsel, 1993, p. 117) that the MLE of the model parameters are stongly consistent and asymptotically normally distributed. Here MLE denotes estimates obtained by maximizing the multivariate normal density function. Next, we discuss more on the impulse response functions of VARMA models and introduce the forecast error variance decomposition.