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Abstract
The dissertation consists of three chapters, each of which is titled Predictive Quantile Regression with Persistent Covariates , Predictive Regression under Various Degrees of Persistence and Robust Long-Horizon Regression and Martingale Decomposition and Approximation for Nonlinear Dependent Processes.
Predictive regression models are extensively used in empirical macroeconomics and finance. A leading example is stock return regression where predictability has been a long standing puzzle and the literature is now vast. Forward premium regressions and consumption growth regressions are other forecast models that similarly present empirical puzzles. A central econometric issue in all these models is severe size distortion under the null arising from the presence of persistent predictors coupled with weak discriminatory power in detecting marginal levels of predictability.
The first two chapters of my dissertation seeks to address these issues by developing new methods of inference for predictive regression. They adopt and extend a recent methodology called IVX filtering (Magdalinos and Phillips, 2009b). The idea is to filter a persistent and possibly endogenous predictor to generate an instrument of intermediate persistence which corrects size distortion while maintaining discriminatory power. The first chapter develops the IVX filtering idea in the framework of quantile regression (QR) and proposes a new approach to inference, which we call IVX-QR, with features that are well suited to financial and macroeconomic applications. The second chapter develops a long-horizon version of IVX methods showing that local discriminatory power in prediction can be substantially enhanced in comparison with short-horizon regression.
The last chapter develops martingale decomposition and approximation methods under a new nonlinear dependence measure (Wu, 2005), thereby assisting the limit theory development of many nonlinear time series models.
