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

Author

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  • Francesca Di Iorio

    (Department of Political Science, University of Naples Federico II, via L. Rodinò 22 ,I-80138 Naples, Italy)

  • Umberto Triacca

    (Department of Computer Engineering, Computer Science and Mathematics, University of L'Aquila, via Vetoio, I-67010 Coppito, L'Aquila, Italy)

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.

Suggested Citation

  • Francesca Di Iorio & Umberto Triacca, 2014. "Testing for A Set of Linear Restrictions in VARMA Models Using Autoregressive Metric: An Application to Granger Causality Test," Econometrics, MDPI, vol. 2(4), pages 1-14, December.
    • Handle: RePEc:gam:jecnmx:v:2:y:2014:i:4:p:203-216:d:43816
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    References listed on IDEAS

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