  We propose sequential Monte Carlo based algorithms for maximum likelihood
estimation of the static parameters in hidden Markov models with an intractable
likelihood using ideas from approximate Bayesian computation. The static
parameter estimation algorithms are gradient based and cover both offline and
online estimation. We demonstrate their performance by estimating the
parameters of three intractable models, namely the alpha-stable distribution,
g-and-k distribution, and the stochastic volatility model with alpha-stable
returns, using both real and synthetic data.
