Essays on Nonstationary Econometrics

My dissertation consists of four essays which contribute new theoretical results to robust inference procedures and machine learning algorithms in nonstationary models. Chapter 2 compares the asymptotic efficiency between the OLS and the detrending GLS estimates in the model with integrated errors. The limiting distributions are derived for pure explosive, mildly explosive, mildly stationary, and local-to-unity time series models. For the local-to-unity case, when the distance parameter is higher than a cut-off value, both the asymptotic bias and variance of the OLS estimate is smaller than the GLS counterpart. Chapter 3 proposes novel mechanisms for identifying explosive bubbles in panel autoregressions with a latent group structure. The first approach applies a recursive k-means clustering algorithm to explosive panel autoregressions. The second approach uses a modified k-means clustering algorithm for mixed-root panel autoregressions. We establish the uniform consistency of both clustering algorithms. The abovementioned k-means procedures achieve the oracle properties so that the post-classification estimators are asymptotically equivalent to the infeasible estimators that use the true group identities. A panel recursive procedure is proposed to estimate the origination date of explosiveness. Finally, the proposed method is applied to China’s real estate market and generates some impressive empirical results. Chapter 4 explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a broad class of persistent and time-varying stochastically nonstationary regressors. The asymptotic distributions of the IVX estimators are new compared to previous work but again lead to pivotal limit distributions for Wald testing procedures that remain robust for both single and multiple regressors with various degrees of persistence and stochastic and fixed local departures from unity. The new methods are illustrated in an empirical application to evaluate the predictive capability of economic fundamentals in forecasting excess returns in the Dow Jones industrial average index. Chapter 5 examines the law of iterated logarithm (LIL) for near-unity processes. For the first time, this paper rigorously prove the LILs of various nonstationary processes whose roots are in the vicinity of unity, including mildly stationary, mildly explosive, and local-to-unity cases. The LILs of sample moments on mildly explosive and mildly stationary processes are also provided in this chapter.