Measuring Nonstationary Cycles: a Time-Deformation Approach

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Title: Measuring Nonstationary Cycles: a Time-Deformation Approach
Author: Movchan, Oleksandr Victorovich
Advisors: Dr. John J. Seater, Committee Member
Dr. Atsushi Inoue, Committee Chair
Dr. Denis Pelletier, Committee Co-Chair
Dr. David A. Dickey, Committee Member
Abstract: This dissertation consists of three essays on modeling and parameter estimation for covariance non-stationary processes. The first essay considers the non-linear deformation of time scale for G(lambda)-stationary processes developed by Jiang, Gray and Woodward [2006]. After the appropriate Box-Cox transformation, processes which are nonstationary in the regular time domain, become stationary in the transformed time scale, thus allowing application of traditional econometric tools. We also study the consistency properties of the Q-statistic which is used to estimate parameters of time deformation connecting regular and transformed time scales. As an empirical illustration, the cyclical behavior of the U.S. unemployment series is studied in the context of a structural time series model with explicit trend and cycle modeling. Fitting the model in the deformed time provides different frequency estimates as well as improved inference statistic comparing to the model estimated in the regular time domain. Second essay investigates the case when the parameters of time deformation for G(lambda)-stationary processes are time-varying, thereby allowing cyclical behavior to vary over the observed data interval. Forecast of unemployment series performed in the deformed time with varying frequencies provides a better fit to the data over the long-term forecasting horizon. We also estimate the dynamics of parameter lambda and show that it can be modeled by first-order Markov chain process. While there are many works considering application of Markov-switching models to macroeconomics series, our approach is different in the sense that we consider regime shifts not in the original data, but in the time scale along which the data is measured. In the last essay we consider Method of Moments (MM) as an alternative approach for the parameter estimation in State Space models (SSM). Estimation and inference in non-Gaussian or non-linear models is usually carried out using importance sampling or Monte Carlo simulation methods. Our method is different in the way that it allows us to relax the assumptions about the data distribution or about the potential non-linearity embedded into the model. Thus, it can be used as the general tool for models of unknown or not tractable form. At the same time our approach appears to be more efficient since it does not require analytical or computational solution for the approximating models, and does not rely on simulation or sampling techniques. Using Kalman filter and smoother equations, we derive a set of moment conditions, and investigate performance of MM estimation in the series of Monte Carlo simulations for common types of SSM, as well as for several empirical examples described in literature. Our results indicate that Method of Moments provides adequate results for the regular Gaussian linear SSM. At the same time, for non-Gaussian and non-linear models our approach can compete with Bayesian and importance sampling estimation methods.
Date: 2009-11-24
Degree: PhD
Discipline: Economics

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