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## WHAT IS THE CANONICAL HIDDEN NON-MARKOV PROCESS?

Hidden Markovian models are highly developed, and there is a large literature for the SV model and its parameter estimation. But the problem is that the right model for stochastic volatility is a long memory model; it is not the well-developed ARFIMA model however. It is a Mittag-Leffler model:

$r_t = e^{h_t/2} \epsilon_t$

$\epsilon_t \sim N(0,1)$

$h_t = d*MittagLeffer(-c*t^a,a,b)$

So the Jacquier-Polson-Rossi 1994-type work needs to find an analogue for this case. Of course the underlying state equation is long memory so the standard state space models do not apply directly. At the same time, the number of parameters is four in this case. This looks like an important problem because it is quite likely that equity volatility is not the only process where MittagLeffler type long memory is a better fit to actual data than ARFIMA.