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Testing for Noncausal Vector Autoregressive Representation

Hamidi Sahneh, Mehdi (2013): Testing for Noncausal Vector Autoregressive Representation.

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Abstract

We propose a test for noncausal vector autoregressive representation generated by non-Gaussian shocks. We prove that in these models the Wold innovations are martingale difference if and only if the model is correctly specified. We propose a test based on a generalized spectral density to check for martingale difference property of the Wold innovations. Our approach does not require to identify and estimate the noncausal models. No specific estimation method is required, and the test has the appealing nuisance parameter free property. The test statistic uses all lags in the sample and it has a convenient asymptotic standard normal distribution under the null hypothesis. A Monte Carlo study is conducted to examine the �finite-sample performance of our test.

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