Robust inference in AR-G/GARCH models under model uncertainty

Abstract

This paper provides a robust test for a function of the autoregressive parameters in AR models driven by G/GARCH noise under model uncertainty in an asymptotic framework. To address this method, we adopt the model average and choose weights based on our Mallows-type methods. We next present a valid confidence interval by dividing the sample into a fixed number of groups to form a normalized estimator which is asymptotically related to the Student’s t-distribution. We derive asymptotic results that are not only interesting in their own right, but contribute to the theoretical foundations. These results include limiting distributions of the proposed Mallows-type model averaging and selection estimators. The proposed averaging estimators are stable-family distributions and are yet to be precisely characterized; hence they cannot be implemented by simulation. Through simulation experiments, our method yields outstanding numerical performance, especially for testing the quotient of coefficients in finite-sample tests.