Bootstrapping autoregression under non-stationary volatility

This paper studies robust inference in autoregression around a polynomial trend with stable autoregressive roots under non-stationary volatility. The formulation of the volatility process is quite general including many existing deterministic and stochastic non-stationary volatility specifications. The aim of the paper is two-fold. First, it develops a limit theory for least squares estimators and shows how non-stationary volatility affects the consistency, convergence rates and asymptotic distributions of the slope and trend coefficients estimators in different ways. This complements the results recently obtained by Chung and Park (2007, Journal of Econometrics 137, 230–59. Second, it studies the recursive wild bootstrap procedure of Gonçalves and Kilian (2004, Journal of Econometrics 123, 89–120) in the presence of non-stationary volatility, and shows its validity when the estimates are asymptotically mixed Gaussian. Simulations are performed to compare favourably the recursive wild bootstrap with other inference procedures under non-stationary volatility.