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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.
Econometrics 2014, 2(4), 203-216; https://doi.org/10.3390/econometrics2040203
Received: 8 September 2014 / Revised: 30 October 2014 / Accepted: 3 December 2014 / Published: 22 December 2014
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
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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