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Inferences in stochastic volatility models: a new simpler way. (English) Zbl 1407.62329

Sutradhar, Brajendra C. (ed.), Advances and challenges in parametric and semi-parametric analysis for correlated data. Proceedings of the 2015 international symposium in statistics, ISS 2015, St. John’s, Canada, July 6–8, 2015. Cham: Springer. Lect. Notes Stat. 218, 97-131 (2016).
Summary: Two competitive analytical approaches, namely, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are widely used in statistics and econometrics literature for inferences in stochastic volatility models (SVMs). Alternative numerical approaches such as Monte Carlo Markov chain (MCMC), simulated maximum likelihood (SML) and Bayesian approaches are also available. All these later approaches are, however, based on simulations. In this paper, we revisit the analytical estimation approaches and briefly demonstrate that the existing GMM approach is unnecessarily complicated. Also, the asymptotic properties of the likelihood approximation based QML approach are unknown and the finite sample based QML estimators can be inefficient. We then develop a precise set of moment estimating equations and demonstrate that the proposed method of moments (MM) estimators are easy to compute and they perform well in estimating the parameters of the SVMs in both small and large time series set up. A ‘working’ generalized quasi-likelihood (WGQL) estimation approach is also considered. Estimation methods are illustrated by reanalyzing a part of the Swiss-Franc and U.S. dollar exchange rates data.
For the entire collection see [Zbl 1347.62015].

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E15 Exact distribution theory in statistics

Software:

STAMP ; FinTS
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