The aim of this paper is to study the local approximate maximum likelihood estimations of time-varying stochastic volatility (SV) model. The approximate log-transition density functions of the SV model are obtained by using the Hermite and Kolmogorov methods. The performance of the approximate transition probability density is demonstrated by Choi (2015). The approximate maximum likelihood estimations (MLE) are obtained by the approximate log-transition density functions. We prove the asymptotic properties of the approximate logtransition density of the SV model.
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