Partially observed microstructure models, containing stochastic volatility, dynamictrading noise, and short-term inertia, are introduced to address the following questions:(1) Do the observed prices exhibit statistically significant inertia? (2) Isstochastic volatility (SV) still evident in the presence of dynamical trading noise? (3)If stochastic volatility and trading noise are present, which SV model matches theobserved price data best? Bayes factor methods are used to answer these questionswith real data and this allows us to consider volatility models with very differentstructures. Nonlinear filtering techniques are utilized to compute the Bayes factoron tick-by-tick data and to estimate the unknown parameters. It is shown thatour price data sets all exhibit strong evidence of both inertia and Heston-typestochastic volatility.
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