Three Essays on Nonstationary Time Series Analysis

TL;DRAbstract

Financial and macroeconomic time series data are often nonstationary. My dissertation consists of three essays concerning time series models with nonstationarity. Chapter 1 develops a new jackknife estimator for nonstationary autoregressive model. The remaining two chapters explore the restricted maximum likelihood (REML hereafter) estimation and the restricted maximum likelihood based likelihood ratio test (RLRT hereafter) in predictive regression. Chapter 1 proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known to suffer from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently, Chambers and Kyriacou (2013) introduces a new jackknife method to remove the first order bias in the estimator of the persistence parameter in a discrete ti

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