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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, January 20, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Tze Lai}
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\centerline{\bf Dynamic Models with Time-Varying Volatilities and 
Regression Parameters and}
\centerline{\bf Their Applications to Financial Time Series }
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Abstract:

Volatility modeling is a cornerstone of empirical finance, as portfolio
theory, asset pricing and hedging all involve volatilities, and its
fundamental importance has been recognized in this year's Nobel Prize
award in Economics. After a brief review of conventional approaches to
modeling asset returns and their volatilities, we describe a new class
of
dynamic models that are stochastic regression models in which the
regression parameters and error variances may undergo abrupt changes at
unknown time points, while staying constant between adjacent
change-points. Assuming conjugate priors, we derive closed-form
recursive
Bayes estimates of the regression parameters and error variances.
Approximations to the Bayes estimates are developed that have much lower
computational complexity and yet are comparable to the Bayes estimates
in statistical efficiency. We also address the problem of unknown
hyperparameters and propose two practical methods for simultaneous
estimation of the hyperparmeters, regression parameters and error
variances. Applications of the methodology to simulated and real
financial data show that it offers a promising alternative approach to
modeling and forecasting asset returns and their volatilities.

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