Testing for A Set of Linear Restrictions in VARMA Models\ud Using Autoregressive Metric: An Application to Granger\ud Causality Test

摘要

In this paper we propose a test for a set of linear restrictions in a Vector\udAutoregressive Moving Average (VARMA) model. This test is based on the autoregressive\udmetric, a notion of distance between two univariate ARMA models, M0 and M1, introduced\udby Piccolo in 1990. In particular, we show that this set of linear restrictions is equivalent to a\udnull distance d(M0;M1) between two given ARMA models. This result provides the logical basis for using d(M0;M1) = 0 as a null hypothesis in our test. Some Monte Carlo evidence\udabout the finite sample behavior of our testing procedure is provided and two empirical examples are presented.