Unified Inference for an AR Process Regardless of Finite or Infinite Variance GARCH Errors*

Abstract

Statistical inference in finance often depends on certain moment conditions such as finite or infinite variance, yet it is practically challenging to disentangle these conditions. This article develops a class of unified unit root tests for AR(1) models and a weighted least squares estimator along with robust inference for a stationary AR(r) model regardless of finite or infinite variance GARCH errors. The inferential framework applies the empirical likelihood method to some weighted score equations without estimating the GARCH errors. In contrast to extant unit root tests relying on bootstrap or subsampling methods to approximate critical values, the proposed unit root tests can be easily implemented with critical values obtained directly from a chi-squared distribution using the Wilks theorem. Extensive simulation studies confirm the good finite sample performance of the proposed methods before we illustrate them empirically with financial ratios for stock return predictability and HKD/USD exchange rate returns.