Essays in Time Series Econometrics

Abstract

This collection of essays investigates robust inference and modelling in time series econometrics. Chapter 1 considers the problem of deriving heteroskedasticity and autocorrelation robust (HAR) inference about a scalar parameter of interest. The main finding implies that, for a given sample size, one can only be confident about the efficiency of a valid HAR test if we are willing to make a priori assumptions about the persistence properties of the data. This chapter demonstrates that it is advantageous to allow for bias in long-run variance estimation and adjust the critical value to explicitly account for the maximum bias. Chapter 2, jointly with Ulrich Mueller, proposes a flexible asymptotic framework for the modelling of persistent time series, by generalizing the popular local-to-unity model. We establish the richness of the class of this generalized local-to-unity model, GLTU(p), in the sense that their limiting pro-cesses can well approximate a large class of stationary Gaussian processes in the total variation norm. This chapter also suggests a straightforward approximation to the limited-information asymptotic likelihood of the GLTU(p) model. Chapter 3 applies the econometric framework developed in Chapter 2 to examine and document the persistence properties of 9 macroeconomic time series over 17 advanced economies, based on the Jorda-Schularick-Taylor Macrohistory Database. It is found that allowing for the generality in modelling long-range dependence can substantially alter quantitative statements about the persistence of macroeconomic time series. Based on empirical evidence, this chapter recommends using an appropriately defined measure of the half-life in the GLTU(p) model to gauge the persistence of macroeconomic time series.