Witte, Hugh Douglas; PhD
THE UNIVERSITY OF ARIZONA, 1999
ECONOMICS, FINANCE (0508); STATISTICS (0463)
In this paper we exploit some recent computational advances in Bayesian inference,
coupled with data
augmentation methods, to estimate and test continuous-time stochastic volatility
models. We augment
the observable data with a latent volatility process which governs the evolution
of the data's volatility. The
level of the latent process is estimated at finer increments than the data are
observed in order to derive a
consistent estimator of the variance over each time period the data are measured.
The latent process
follows a law of motion which has either a known transition density or an approximation
to the transition
density that is an explicit function of the parameters characterizing the stochastic
differential equation.
We analyze several models which differ with respect to both their drift and
diffusion components. Our
results suggest that for two size-based portfolios of U.S. common stocks, a
model in which the volatility
process is characterized by nonstationarity and constant elasticity of instantaneous
variance (with respect
to the level of the process) greater than 1 best describes the data. We show
how to estimate the various
models, undertake the model selection exercise, update posterior distributions
of parameters and
functions of interest in real time, and calculate smoothed estimates of within
sample volatility and
prediction of out-of-sample returns and volatility. One nice aspect of our approach
is that no
transformations of the data or the latent processes, such as subtracting out
the mean return prior to
estimation, or formulating the model in terms of the natural logarithm of volatility,
are required.
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