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Econometrics 2014, 2(4), 203-216; doi:10.3390/econometrics2040203

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

1
Department of Political Science, University of Naples Federico II, via L. Rodinò 22 ,I-80138 Naples, Italy
2
Department of Computer Engineering, Computer Science and Mathematics, University of L'Aquila, via Vetoio, I-67010 Coppito, L'Aquila, Italy
*
Author to whom correspondence should be addressed.
Received: 8 September 2014 / Revised: 30 October 2014 / Accepted: 3 December 2014 / Published: 22 December 2014
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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, M0 and M1, 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(M0,M1) = 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. View Full-Text
Keywords: VARMA; linear restriction; autoregressive metric; bootstrap VARMA; linear restriction; autoregressive metric; bootstrap
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Di Iorio, F.; Triacca, U. Testing for A Set of Linear Restrictions in VARMA Models Using Autoregressive Metric: An Application to Granger Causality Test. Econometrics 2014, 2, 203-216.

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