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## SO WHAT IS WRONG WITH STOCHASTIC VOLATILITY MODELS?

Stochastic volatility models are extremely strong models empirically, and an excellent account of their origins and research can be found in Torben Andersen and Neil Shephard’s paper Andersen-Shephard-SVOrigins-2008.  Our findings of the universality of Mittag-Leffler fits to autoregressive coefficients of volatility across instruments and frequencies for $\log(ret^2)$ and their denoised versions:  equities, gold, crude oil daily frequency and US inflation monthly frequency and our expectation that this is universally valid shows that the stochastic volatility models are misspecified in the sense that the latent volatility process in nature does not follow a MARKOVIAN process but one that can be approximated by a MARKOVIAN finte order autoregression.  Thus in a sense the hard work in Bayesian estimation or other complex estimation schemes are technically misspecifying the undelying process by a MARKOVIAN APPROXIMATION which has good out-of-sample forecasting properties nonetheless.  The actual latent process in nature for all these stochastic volatility models are non-Markovian and their innovations have a specific Mittag-Leffler decay structure for a finite order autoregressive model, which implies that the correct model is approximable by Markovian autoregressions.

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