Minimum Hellinger distance estimates of a multivariate autoregressive model. Application to the EXPARMA model

We consider an autoregressive model {X(t), t epsilon Z}, which takes values in R(m), m > 1, and which is defined as follows: X(t) = H(t)heta(X(t-1)) + e(t) where {e(t), t epsilon Z} is a sequence of random vectors in R(m), independent and identically distributed. H-0 : Theta x R(m) --> R(m) is a measurable function and Theta subset of R(d), d greater than or equal to 1. The purpose of this Note is to give an estimate of the parameter theta by the minimum Hellinger distance method. We establish, under mild conditions, limit theorems of this estimate. As an example, we apply these results to the EXPARMA model.