CEBA talks 2020-2021
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Uniform and distribution-free inference with general autoregressive processes

Authors:  T. Magdalinos and K. Petrova (Universitat Pompeu Fabra) 

Abstract: A unified theory of estimation and inference is developed for an autoregressive process with root in [-1+δ,∞) for some δ>0 that includes the stable, unstable, explosive and all intermediate regions. The discontinuity of the limit distribution of the t-statistic along autoregressive regions and its dependence on the distribution of the innovations in the explosive region (1,∞) are addressed simultaneously. A novel estimation procedure, based on a data-driven combination of a near-stationary and a mildly explosive instrument, delivers an asymptotic mixed-Gaussian theory of estimation and gives rise to an asymptotically standard normal t-statistic across all autoregressive regions independently of the distribution of the innovations. The resulting hypothesis tests and confidence intervals are shown to have correct asymptotic size (uniformly over the parameter space) both in autoregressive and in predictive regression models, thereby establishing a general and unified framework of inference with autoregressive processes. Extensive Monte Carlo experimentation shows that the proposed methodology exhibits very good finite sample properties over the entire autoregressive parameter space and compares favourably to existing methods within their parametric [-1+δ,1] validity range. We apply our procedure to the estimation of the early growth rates of Covid-19 infections across countries by employing a stochastic SIR model and constructing confidence intervals for the epidemic's basic reproduction number without a priory knowledge of the model's stability/explosivity properties.