Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

We hope to be able to provide answers to the following questions: 1) Has there been a structural break in postwar U.S. real GDP growth toward more stabilization? 2) If so, when would it have been? 3) What's the nature of the structural break? For this purpose, we employ a Bayesian approach to dealing with structural break at an unknown changepoint in a Markov-switching model of business cycle. Empirical results suggest that there has been a structural break in U.S. real GDP growth toward more stabilization, with the posterior mode of the break date around 1984:1. Furthermore, we #nd a narrowing gap between growth rates during recessions and booms is at least as important as a decline in the volatility of shocks. Key Words: Bayes Factor, Gibbs sampling, Marginal Likelihood, Markov-Switching, Stabilization, Structural Break. JEL Classi#cations: C11, C12, C22, E32. 1. Introduction In the literature, the issue of postwar stabilization of the U.S. economy relative to the prewar period has...

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This paper analyzes the role of contagion in the currency crises in emerging markets during the 1990s. It employs a non-linear Markov-switching model to conduct a systematic comparison and evaluation of three distinct causes of currency crises: contagion, weak economic fundamentals, and sunspots, i.e. unobservable shifts in agents ’ beliefs. Testing this model empirically through Markov-switching and panel data models reveals that contagion--a high degree of real integration and financial interdependence among countries--is a core explanation for recent emerging market crises. The model has a remarkably good predictive power for the 1997-98 Asian crisis. The findings suggest that in particular the degree of financial interdependence and also real integration among emerging markets are crucial not only in explaining past crises but also in predicting the transmission of future financial crises.

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This paper examines the correlation between stock and bond returns. It first documents that the major trends in stock-bond correlation for G7 countries follow a similar reverting pattern in the past forty years. Next, an asset pricing model is employed to show that the correlation of stock and bond returns can be explained by their common exposure to macroeconomic factors. The link between the stock-bond correlation and macroeconomic factors is examined using three successively more realistic formulations of asset return dynamics. Empirical results indicate that the major trends in stock-bond correlation are determined primarily by uncertainty about expected inflation. Unexpected inflation and the real interest rate are significant to a lesser degree. Forecasting this stock-bond correlation using macroeconomic factors also helps improve investors ’ asset allocation decisions. One implication of this link between trends in stock-bond correlation and inflation risk is the Murphy’s Law of Diversification: diversification opportunities are least available when they are most needed.

Abstract: The popular Nelson-Siegel (1987) yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold and Li (2006) have recently proposed a dynamized version. In this paper we extend Diebold-Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the U.K. and the U.S., we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries.

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assistance was provided by Xifeng Diao. We are very appreciative of financial support provided

We develop a theoretical model to compare forecast uncertainty estimated from time series models to those available from survey density forecasts. The sum of the average variance of individual densities and the disagreement is shown to approximate the predictive uncertainty from well-specified time series models when the variance of the aggregate shocks is relatively small compared to that of the idiosyncratic shocks. Due to grouping error problems and compositional heterogeneity in the panel, individual densities are used to estimate aggregate forecast uncertainty. During periods of regime change and structural break, ARCH estimates tend to diverge from survey measures.