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STICERD Econometrics Seminar Series

Uniform and distribution-free inference with general autoregressive processes

Katerina Petrova (Pompeu Fabra University)

Thursday 02 March 2023 14:00 - 15:30

Many of our seminars and public events this year will continue as in person or as hybrid (online and in person) events. Please check our website listings and Twitter feed @STICERD_LSE for updates.

Unless otherwise specified, in-person seminars are open to the public.

Those unable to join the seminars in-person are welcome to participate via zoom if the event is hybrid.

About this event

A unified theory of estimation and inference is developed for an autoregressive process with root in (-∞, ∞) 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 regions (-∞, -1) ∪ (1, ∞) are addressed simultaneously. A novel estimation procedure, based on a data-driven combination of a near-stationary and a mildly explosive endogenously constructed 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 for 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, 1] validity range. We demonstrate that a first-order difference equation for the number of infections with an explosive/stable root results naturally after linearization of an SIR model at the outbreak and apply our procedure to Covid-19 infections to construct confidence intervals on the model's parameters, including the epidemic's basic reproduction number, across a panel of countries without a priori knowledge of the model's stability/explosivity properties

STICERD Econometrics seminars are held on Thursdays in term time at 14.00-15.30, in SAL 3.05, unless specified otherwise.

Seminar organisers: Professor Tai Otsu and Dr. Vassilis Hajivassiliou.

For further information please contact Sadia Ali:

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