Three Essays on Nonstationary Econometrics

This dissertation consists of three essays that contribute to the theory of nonstationary time-series analysis. The first chapter explores inference procedures for predictive regressions with time-varying deviations from unity. We extend the self-generated instrumentation, called IVX, to incorporate persistent regressors of functional local-to-unity, functional mildly explosive, and functional mildly stationary roots. The asymptotic distributions of IVX estimators under time-varying parameters are novel and nonpivotal but lead to pivotal distributions of the corresponding Wald statistics that are robust across various roots. We also verify the existence of time-varying coefficients and the predictability of fundamentals with such unstable parameters by using the S&P 500 data. The second chapter proposes a functional local-to-unity model with autoregressive coefficients that vary smoothly over time. Two sieve estimators, namely a time series and a panel autoregression estimators, are considered to estimate the local-to-unity function. The property of consistency is established. Besides, a consistent specification test to detect parameter instability is proposed. Finally, we apply the panel estimator and specification test to the price index of China's real estate market and obtain significant empirical results in measuring time-varying growth rates in the data. The third chapter discusses about time-varying predictive regressions, which are useful in the applications of empirical finance. We investigate a nonparametric predictive regression model with mixed-root regressors and time-varying coefficients, evolving smoothly over time. Further, we present a new variant of the self-generated instrument, called Sieve-IVX, which attains robust inference irrespective of various degrees of persistence. We establish its consistency and provide a Wald test to detect the temporary predictability of economic fundamentals.