Three Essays in Econometrics: Multivariate Long Memory Time Series and Applying Regression Trees to Longitudinal Data

The first two chapters of this dissertation discuss multivariate long memory models. First, we discuss two distinct parametric multivariate time-series models. We discuss the implications of the models and describe an extension to fractional cointegration. We describe algorithms for computing the covariances of each model, for computing the likelihood and for simulating from each model. These algorithms are much more computationally efficient than the existing algorithms and are equally accurate, making it feasible to model multivariate long memory time series and to simulate from these models. We use maximum likelihood to fit models to data on goods and services inflation in the United States. Second, we present a semiparametric model for bivariate long-memory time series that allows for power law behavior in the coherency and powers of the frequency in the phase. We describe the implications of a power law in the coherency and of powers of the frequency in the phase on the time-domain behavior of the time series and provide time domain examples. We prove the consistency of the averaged periodogram estimator for estimating the power law in the cross-spectrum and coherency. We prove that the very-narrow-band least squares estimator of the cointegrating parameter is not affected by power laws in the phase and coherency. We apply our methods to money supply data and to high and low stock prices. The final chapter presents a methodology that combines the flexibility of treebased estimation methods with the structure of random effects models for longitudinal data. We apply the resulting model and estimation method, called the RE-EM tree, to state traffic fatality rates and to pricing in online transactions. We also perform extensive simulation experiments to show that the estimator improves predictive performance relative to regression trees without random effects and is comparable or superior to using linear models with random effects.