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

Parameter Estimation in Hidden Markov Models with Intractable Likelihoods Using Sequential Monte Carlo