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

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.

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Year of publication:	2014
Authors:	Di Iorio, Francesca ; Triacca, Umberto
Published in:	Econometrics : open access journal. - Basel : MDPI, ISSN 2225-1146, ZDB-ID 2717594-7. - Vol. 2.2014, 4, p. 203-216
Subject:	VARMA \| linear restriction \| autoregressive metric \| bootstrap \| Kausalanalyse \| Causality analysis \| Bootstrap-Verfahren \| Bootstrap approach \| Zeitreihenanalyse \| Time series analysis \| VAR-Modell \| VAR model \| Schätztheorie \| Estimation theory \| ARMA-Modell \| ARMA model \| Statistischer Test \| Statistical test \| Autokorrelation \| Autocorrelation