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Original Articles

Riemann manifold Langevin methods on stochastic volatility estimation

, &
Pages 7942-7956 | Received 10 Sep 2016, Accepted 20 Oct 2016, Published online: 09 May 2017
 

ABSTRACT

In this article, we perform Bayesian estimation of stochastic volatility models with heavy tail distributions using Metropolis adjusted Langevin (MALA) and Riemman manifold Langevin (MMALA) methods. We provide analytical expressions for the application of these methods, assess the performance of these methodologies in simulated data, and illustrate their use on two financial time series datasets.

MATHEMATICS SUBJECT CLASSIFICATION:

Funding

This research was partially supported by FAPESP grant number 2013/00506-1 for the first author. Ricardo Ehlers received support from São Paulo Research Foundation (FAPESP) - Brazil, under grant number 2015/00627-9.

Notes

1 These results were expected and are in line with the literature, see, for example, Jacquier et al. (Citation1994).

2 The maximum likelihood estimates in Harvey et al. (Citation1994) are , , and , then and . Durbin and Koopman (Citation2001) report the following maximum likelihood estimates: , , and but do not report the Bayesian estimates.

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