Aspects of estimation and inference for predictive regression models

Abstract

This PhD thesis presents three essays on nonstationary time series econometrics which are grouped into three chapters. The chapters cover aspects of estimation and inference for predictive regression models through the lens of moderate deviation principles from the unit root boundary in a class of stable but nearly-unstable processes which exhibit high persistence. The first chapter presents an overview of the research background which includes the persistence classes and the main asymptotic properties of estimators for nonstationary autoregressive processes. The persistence properties of time series is modelled via the local-to-unity parametrization which implies that the autoregressive coefficient is specified such that it approaches the unit boundary as the sample size increases. The second part of the chapter summarizes the structure of the thesis and the main contributions to the literature. The second chapter, proposes an econometric framework for predictability testing in linear predictive regression models robust against parameter instability. In particular, the asymptotic theory for the proposed sup-Wald test statistics when regressors are assumed to be mildly integrated and persistent stochastic processes is established. The asymptotic theory of OLS and IVX based estimators and test statistics presented in this thesis is developed based on standard local-to-unity asymptotics and the limit theory of triangular arrays of martingales. The third chapter, addresses the aspect of structural break detection for nonstationary time series when a conditional quantile specification form is used. In particular, the proposed econometric framework is suitable for testing for a structural break at unknown time in nonstationary quantile predictive regression models and can be further employed for investigating the aspect of quantile predictability against parameter instability. The fourth chapter, proposes a novel estimation and inference methodology in systems of quantile predictive regressions with generated regressors. This econometric framework allows to address the issue of modelling systemic risk in financial networks when considering the interplay between network-type of dependence and time series non stationarity