Abstract:
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In financial time series, an important quantity of interest is the volatility (or variability) of the underlying stochastic process at each time point which is not directly observed. To model this latent series, we develop a stochastic volatility model based on the alpha-stable distribution. The alpha-stable distribution provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling the volatility of financial returns. One difficulty, however, is that the alpha-stable distribution does not have a tractable probability density function. Our newly developed auxiliary particle filter based on approximate Bayesian computation (ABC) addresses this issue. The ABC auxiliary particle filter (ABC-APF) that we propose provides not only a good alternative to state estimation in stochastic volatility models, but it also improves on the existing ABC literature. Our algorithm can easily be applied to any hidden Markov model for which the likelihood function is intractable or computationally expensive. Application of this model to exchange rate series through the various global financial crises is explored.
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