A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter

This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva’s (2007a) modification of Stock’s (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well in finite samples in terms of coverage probability and average length, for innovations with and without conditional heteroskedasticity.

Keywords: Asymptotically similar, Asymptotic size, Autoregressive model, Conditional heteroskedasticity, Confidence interval, Hybrid test, Subsampling test, Unit root

JEL Classification: C12, C15, C22