Limit Theory under Network Dependence and Nonstationarity

TL;DR

This paper provides advanced limit theory results for time series and network econometrics, focusing on nonstationarity, local-to-unity models, and moderate deviation principles, with implications for nonstationary autoregressive processes.

Contribution

It introduces new limit theorems and non-asymptotic results for nonstationary time series and network models, emphasizing eigenvalue behavior and moderate deviations.

Findings

Limit theorems for nonstationary time series regression

Non-asymptotic moderate deviation principles for covariance eigenvalues

Asymptotics for unit root moderate deviations in autoregressive processes

Abstract

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity parametrization when modeling time series nonstationarity. Moreover, we present various non-asymptotic theory results for moderate deviation principles when considering the eigenvalues of covariance matrices as well as asymptotics for unit root moderate deviations in nonstationary autoregressive processes. Although not all applications from the literature are covered we also discuss some open problems in the time series and network econometrics literature.