Stochastic volatility filtering with intractable likelihoods

“The contribution of our work is two-fold: first, we extend the SVM literature, by proposing a new method for obtaining the filtered volatility estimates. Second, we build upon the current ABC literature by introducing the ABC auxiliary particle filter, which can be easily applied not only to SVM, but to any hidden Markov model.”

Another ABC arXival: Emilian Vankov and Katherine B. Ensor posted a paper with the above title. They consider a stochastic volatility model with an α-stable distribution on the observables (or returns). Which makes the likelihood unavailable, even were the hidden Markov sequence known… Now, I find very surprising that the authors do not mention the highly relevant paper of Peters, Sisson and Fan, Likelihood-free Bayesian inference for α-stable models, published in CSDA, in 2012, where an ABC algorithm is specifically designed for handling α-stable likelihoods. (Commented on that earlier post.) Similarly, the use of a particle filter coupled to ABC seems to be advanced as a novelty when many researchers have implemented such filters, including Pierre Del Moral, Arnaud Doucet, Ajay Jasra, Sumeet Singh and others, in similar or more general settings. Furthermore, Simon Barthelmé and Nicolas Chopin analysed this very model by EP-ABC and ABC.  I thus find it a wee bit hard to pinpoint the degree of innovation contained in this new ABC paper

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