ABSTRACT
A vector autoregressive process of order p (VAR(/?)) for a system of K variables Yt = (Yu, Ylt, . . . , YKt)T with N observations is defined as
(2)
and a [ = (au, a2t, . . . , aKt) is a vector of random shocks which are indepen dently, identically, and normally distributed with mean zero and covariance Έ α = E [ a ta f ] for all t, i.e.,
The system of equations (1) can also be defined in terms of backshift oper ators as follows:
where φ(2?) = / — φ ^ — φ2^ ----- -- φρΒΡ, and Β is defined as Bj Yi t = Yij-j. The process is stationary if the roots of the determinantal equation |φ(Ζ?)| = 0 are outside the unit circle.
