Moving averages with random coefficients and random coefficient autoregressive models

Consider the series where are iid -valued random vectors and are random matrices independent of the . Under suitable summability conditions on the , if the distribution of is multivariate regularly varying at ∞ then so is the distribution of the sum. Application is made to stationary solutions of the first order random difference equation in , and to the pth order random difference equation . Under the circumstances where explicit solution of the difference equations is impossible, this provides some information about the form of the solution.