Abstract
This paper considers the estimation and testing problems for the coefficient matrices of vector autoregressive models, including infinite variance processes. The self-weighted generalized empirical likelihood (GEL) estimator and test statistic for the hypotheses of the nonlinear restriction of the parameters are proposed. The limiting distributions of the GEL estimator and test statistic are derived under mild distributional conditions for the innovation processes. The proposed testing procedure does not require any prior information for the nuisance parameters of the process, such as the behavior of the distributional tail of the innovation processes; hence, the results in this paper provide a feasible testing procedure for the hypothesis. Simulation experiments illustrate the finite sample performance of the proposed methods.
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