Three essays on nonstationary time-series analysis and network dynamics - TAO, Yubo (Institutional Knowledge at Singapore Management University, 2019)
My dissertation consists of three essays which contribute new theoretical results to nonstationary time-series analysis and network dynamics. Chapter 2 examines the limit properties of information criteria (such as AIC, BIC, HQIC) for distinguishing between the unit root model and the various kinds of explosive models. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different orders of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the unit root model when data come from the unit root model. When data come from the local-to-unit-root model, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the mildly explosive model in the form of 1 + n^a/n with a in the range of (0,1), all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample. Chapter 3 studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behavior according to specific regions of the parameter space that open up the potential for testing these forms of extreme behavior. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behavior are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behavior. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P 500 index data over 1928-2018 reveals strong evidence against parameter constancy over the whole sample period leading to a long duration of what the model characterizes as extreme behavior in real stock prices. Chapter 4 develops a dynamic covariate-assisted spectral clustering method to uniformly estimate the latent group membership of cryptocurrencies consistently. We show that return inter-predictability and crypto characteristics, including hashing algorithms and proof types, jointly determine the crypto market segmentation. Based on this classification result, it is natural to employ eigenvector centrality to identify a cryptocurrency’s idiosyncratic risk. An asset pricing analysis finds that a cross-sectional portfolio with a higher centrality earns a higher risk premium. Further tests confirm that centrality serves as a risk factor well and delivers valuable information content on cryptocurrency markets.