Two stationary, univariate AR(1) processes are driven by correlated in novation sequences. That is, we observe two processes yt and zt where yt

= yt 1 + t t N(0v)

zt = zt 1+ t t N(0w)

where, as usual, t and t are independent over time, i.e., t and t are independent of t k and of t k for any k > 0However, the innovations of the two processes are contemporaneously cross-correlated, i.e., the two series are subject to a common inuence. In particular, the vector

( t t) has a bivariate normal distribution with variance matrix V =

AAwhere Ais the upper triangular Cholesky component of V. De ne the 2 vector xt time series by xt = A1 yt zt Show that xt is a VAR2(1) process and identify the resulting 2 2 AR parameter matrix and innovations variance matrix. Discuss the impli cations, and comment on the assertion of a modeler who argues that we can always use a diagonal innovations variance matrix in VARq(1)

models: do you agree?