Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling

• Verfasst von: Neddermeyer, Jan Christoph [VerfasserIn]
• Titel: Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling
• Verf.angabe: Jan C. Neddermeyer
• E-Jahr: 2011
• Jahr: 15 Feb 2011
• Umfang: 19 S.
• Fussnoten: Gesehen am 21.09.2022
• Titel Quelle: Enthalten in: The journal of statistical computation and simulation
• Ort Quelle: London [u.a.] : Taylor & Francis, 1972
• Jahr Quelle: 2011
• Band/Heft Quelle: 81(2011), 11, Seite 1361-1379
• ISSN Quelle: 1563-5163
• DOI: doi:10.1080/00949655.2010.485315
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: general state-space model
• Sach-SW: high frequency
• Sach-SW: multivariate frequency polygon
• Sach-SW: multivariate stochastic volatility
• Sach-SW: nonparametric density estimation
• Sach-SW: sequential Monte Carlo
• K10plus-PPN: 1817213865

Abstract

Sequential Monte Carlo methods (also known as particle filters and smoothers) are used for filtering and smoothing in general state-space models. These methods are based on importance sampling. In practice, it is often difficult to find a suitable proposal which allows effective importance sampling. This article develops an original particle filter and an original particle smoother which employ nonparametric importance sampling. The basic idea is to use a nonparametric estimate of the marginally optimal proposal. The proposed algorithms provide a better approximation of the filtering and smoothing distributions than standard methods. The methods’ advantage is most distinct in severely nonlinear situations. In contrast to most existing methods, they allow the use of quasi-Monte Carlo (QMC) sampling. In addition, they do not suffer from weight degeneration rendering a resampling step unnecessary. For the estimation of model parameters, an efficient on-line maximum-likelihood (ML) estimation technique is proposed which is also based on nonparametric approximations. All suggested algorithms have almost linear complexity for low-dimensional state-spaces. This is an advantage over standard smoothing and ML procedures. Particularly, all existing sequential Monte Carlo methods that incorporate QMC sampling have quadratic complexity. As an application, stochastic volatility estimation for high-frequency financial data is considered, which is of great importance in practice. The computer code is partly available as supplemental material.