Uniform and Distribution-Free Inference with General Autoregressive Processes

Seminar abstract

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 linearisation 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.

How to attend this seminar

This seminar is free to attend with no need to register in advance.

We welcome you to join us on Wednesday 25 January at 3pm on the Colchester campus room EBS.2.14.

If you are unable to make it in person the session will be live online. Please contact the organiser for detail to join online.

Speaker bio

Professor Tassos Magdalinos

Tassos Magdalinos is currently a Professor of Econometrics at the University of Southampton, having held previous positions at the University of Nottingham and the University of York. His research interests are in the area of time series econometrics with particular focus on uniform inference with mixtures of stationary and nonstationary time series, representation and limit theory for cointegrated systems with mixed stochastic components, explosive and long memory processes, and robust hypothesis tests for stock return predictability. He has published in a number of peer-reviewed journals such as Econometric Theory, the Journal of Econometrics and the Review of Financial Studies. His research has received funding from the ESRC and he is an associate editor of Econometric Theory and of the Journal of Time Series Analysis.