Whittle parameter estimation for vector ARMA models with heavy-tailed noises

This paper studies the Whittle estimation for vector autoregressive and moving average (ARMA) models with heavy-tailed noises. It is shown that the Whittle estimator is consistent with the rate of convergence n(1/alpha) (L) over tilde (n) and its limiting distribution is a function of two stable random vectors, where (L) over tilde (n) is a slowly varying function and alpha is an element of (0, 2) is the tail index of heavy-tailed vector noise. A simulation study is carried out to assess the performance of this estimator in finite samples and a real example is given. This paper includes several limiting theorems for the general heavy-tailed vector processes, which is independent of interest. (C) 2021 Elsevier B.V. All rights reserved.