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222
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... 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 biosequence analysis, and KFMs have bee ..."
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Cited by 579 (3 self)
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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 biosequence 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) linearGaussian. 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 RaoBlackwellised 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.
An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns
 Journal of Financial Economics
, 2004
"... The returns to hedge funds and other alternative investments are often highly serially correlated, in sharp contrast to the returns of more traditional investment vehicles such as longonly equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and s ..."
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Cited by 99 (4 self)
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The returns to hedge funds and other alternative investments are often highly serially correlated, in sharp contrast to the returns of more traditional investment vehicles such as longonly equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure, i.e., investments in securities that are not actively traded and for which market prices are not always readily available. For portfolios of illiquid securities, reported returns will tend to be smoother than true economic returns, which will understate volatility and increase riskadjusted performance measures such as the Sharpe ratio. We propose an econometric model of illiquidity exposure and develop estimators for the smoothing profile as well as a smoothingadjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedgefund style categories and may be a useful proxy for quantifying illiquidity exposure.
Measuring Business Cycles: A Modern Perspective
 The Review of Economics and Statistics
, 1996
"... Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived intere ..."
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Cited by 90 (11 self)
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Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived interest in each attribute separately, and we survey this work. Notable empirical contributions are dynamic factor models that have a single common macroeconomic factor and nonlinear regimeswitching models of a macroeconomic aggregate. We conduct an empirical synthesis that incorporates both of these features. It is desirable to know the facts before attempting to explain them; hence, the attractiveness of organizing businesscycle regularities within a modelfree framework. During the first half of this century, much research was devoted to obtaining just such an empirical characterization of the business cycle. The most prominent example of this work
Bayesian methods for hidden markov models
 Journal of the American Statistical Association
"... ..."
Markovian Models for Sequential Data
, 1996
"... Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We firs ..."
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Cited by 87 (2 self)
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Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, InputOutput HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variablelength Markov models and Markov switching statespace models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...
Nonlinear Gated Experts for Time Series: Discovering Regimes and Avoiding Overfitting
, 1995
"... this paper: ftp://ftp.cs.colorado.edu/pub/TimeSeries/MyPapers/experts.ps.Z, ..."
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Cited by 86 (5 self)
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this paper: ftp://ftp.cs.colorado.edu/pub/TimeSeries/MyPapers/experts.ps.Z,
Term Structure of Interest Rates with Regime Shifts
 Journal of Finance
, 2002
"... We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifi ..."
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Cited by 81 (1 self)
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We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the welldocumented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles. MANY PAPERS DOCUMENT THAT THE UNIVARIATE short interest rate process can be reasonably well modeled in the time series as a regime switching process ~see Hamilton ~1988!, Garcia and Perron ~1996!!. In addition to this statistical evidence, there are economic reasons as well to believe that regime shifts are important to understanding the behavior of the entire yield curve. For example, business cycle expansion and contraction “regimes ” potentially
Switching Kalman Filters
, 1998
"... We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results ..."
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Cited by 60 (3 self)
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We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results on learning using EM in the nonswitching case [DRO93, GH96a] and in the switching, but fully observed, case [Ham90]. 1 Introduction Dynamical systems are often assumed to be linear and subject to Gaussian noise. This model, called the Linear Dynamical System (LDS) model, can be defined as x t = A t x t\Gamma1 + v t y t = C t x t +w t where x t is the hidden state variable at time t, y t is the observation at time t, and v t ¸ N(0; Q t ) and w t ¸ N(0; R t ) are independent Gaussian noise sources. Typically the parameters of the model \Theta = f(A t ; C t ; Q t ; R t )g are assumed to be timeinvariant, so that they can be estimated from data using e.g., EM [GH96a]. One of the main adva...
Robustness and Pricing with Uncertain Growth
 REV. FINANC. STUD
, 2000
"... We study how decision makers' concerns about robustness affect prices and quantities in a stochastic growth model. In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks. An investor observes movements in the technology level but cann ..."
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Cited by 41 (6 self)
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We study how decision makers' concerns about robustness affect prices and quantities in a stochastic growth model. In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks. An investor observes movements in the technology level but cannot perfectly distinguish their sources. Instead the investor solves a signal extraction problem. We depart from most of the macroeconomics and finance literature by presuming that the investor treats the specification of technology evolution as an approximation. To promote a decision rule that is robust to model misspecification, an investor acts as if a malevolent player threatens to perturb the actual data generating process relative to his approximating model. We study how a concern about robustness alters asset prices. We show that the dynamic evolution of the riskreturn tradeoff is dominated by movements in the growthstate probabilities and that the evolution of the dividendprice ratio is driven primarily by the capitaltechnology ratio.
A Comparison of the Forecast Performance of MarkovSwitching and Threshold Autoregressive models of US GNP
 Econometrics Journal
, 1997
"... While there has been a great deal of interest in the modelling of nonlinearities in economic time series, there is no clear consensus regarding the forecasting abilities of nonlinear time series models. We evaluate the performance of two leading nonlinear models in forecasting postwar US GNP, th ..."
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Cited by 37 (9 self)
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While there has been a great deal of interest in the modelling of nonlinearities in economic time series, there is no clear consensus regarding the forecasting abilities of nonlinear time series models. We evaluate the performance of two leading nonlinear models in forecasting postwar US GNP, the selfexciting threshold autoregressive model and the Markovswitching autoregressive model. Two methods of analysis are employed: an empirical forecast accuracy comparison of the two models, and a Monte Carlo study. The latter allows us to control for factors that may otherwise undermine the performance of the nonlinear models. 1 Introduction In recent years there has been a great deal of interest in the modelling of nonlinearities in economic time series. While the usefulness of linear timeseries models in the tradition of Box and Jenkins (1970) is usually gauged by their predictive ability, there does not appear to be a clear consensus as to whether allowing for nonlinearities has l...