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

Francesca Di Iorio and Umberto Triacca
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Umberto Triacca: Department of Computer Engineering, Computer Science and Mathematics, University of L'Aquila, via Vetoio, I-67010 Coppito, L'Aquila, Italy

Econometrics, 2014, vol. 2, issue 4, 1-14

Abstract: In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M 0 and M 1 , introduced by Piccolo in 1990. In particular, we show that this set of linear restrictions is equivalent to a null distance d (M0,M1 ) between two given ARMA models. This result provides the logical basis for using d ( M 0 ,M 1 ) = 0 as a null hypothesis in our test. Some Monte Carlo evidence about the finite sample behavior of our testing procedure is provided and two empirical examples are presented.

Keywords: VARMA; linear restriction; autoregressive metric; bootstrap (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2014
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