The course deals with asymptotic and bootstrap methods for econometric models, with emphasis on inference (estimation and testing) using time series data. The aim is to let the student familiarize with classical issues arising during the specification of an econometric model: testing the underlying assumptions, choosing a useful asymptotic theory to approximate the finite sample behavior of estimator and tests statistics, and improve inference through a correct implementation of the bootstrap.
As reference case, we consider simple time series models allowing for transitory (stationarity) and permanent shocks (unit roots and cointegration). Several tests and bootstrap methods will be presented and discussed.
Preliminaries: it is suggested that students have a background in statistical inference (theory of point estimation and tests of statistical hypothesis), probability (basics and elements of stochastic processes), time series.
Topic 1. Stationarity, Non-stationary time series and unit root testing
Introduction to linear stationary and non-stationary time series models. Unit root testing. Basic asymptotic theory. Power issues, specification issues and the role of deterministic trends. Co-integration: representation and testing.
Topic 2. Introduction to the bootstrap for stationary data
Introduction. Bootstrap hypothesis testing. Bootstrapping stationary time series: the finite order AR case. Bootstrap AR(\infty) processes: sieve bootstrap and block bootstrap. Dealing with heteroskedasticity.
Topic 3. Bootstrap methods for non-stationary data
Inconsistency of the bootstrap under a unit root. Bootstrap unit root tests: the iid case. Bootstrap unit root tests in the AR(\infty) case: sieve and block bootstrap unit root tests. Dealing with deterministic components. The bootstrap in co-integrated models: rank determination and hypotheses on the co-integration vectors.
Topic 4. Further topics in the analysis of time series data
Volatility breaks in nonstationary time series models. Inference under volatility breaks. Disentangling volatility breaks and non-stationarity: wild bootstrap unit root tests. Extension to co-integration. Dealing with infinite variance innovations: inconsistency of the i.i.d. bootstrap, wild bootstrap and permutation bootstrap.