Generalized empirical likelihood specification test robust to local misspecification

It is well known that many of the standard specification tests may not be robust when the alternative is misspecified. This study analyzes a robust specification test for generalized empirical likelihood (GEL) estimators in a weakly dependent time series setting. We show that the usual score test statistic asymptotically follows a non-central chi-square distribution under the local misspecification in the GEL framework. Thus, it spuriously rejects the null hypothesis too frequently. We propose a robust score specification test that asymptotically follows a central chi-square distribution under the local misspecification. A Monte Carlo simulation verifies the usefulness of the proposed tests.