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On-line Bayesian estimation of AR signals in symmetric alpha-stable noise

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Abstract

In this paper we propose an on-line Bayesian filtering and smoothing method for time series models with heavy-tailed alpha-stable noise, with a particular focus on TVAR models. alpha-stable processes have been shown in the past to be a good model for many naturally occurring noise sources. We first point out how a filter that fails to take into account the heavy-tailed character of the noise performs poorly and then examine how an alpha-stable based particle filter can be devised to overcome this problem. The filtering methodology is based on a scale mixtures of normals (SMiN) representation of the alpha-stable distribution, which allows efficient Rao-Blackwellised implementation within a conditionally Gaussian framework, and requires no direct evaluation of the alpha-stable density, which is in general unavailable in closed form. The methodology is shown to work well, outperforming the traditional Gaussian methods both on simulated data and on real audio data sets.

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Bibliographic Info

Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2004_05.

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Length: 32 pages
Date of creation: 01 May 2004
Date of revision:
Publication status: Published in Signal Processing, IEEE Transactions on, Feb. 2006, 54, 2: 775-779. doi: 10.1109/TSP.2005.861886
Handle: RePEc:fir:econom:wp2004_05

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Keywords: Particle filters; Kalman filter; Alpha-stable distributions; Scale mixture of normals.;

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References

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  1. Godsill, Simon J. & Doucet, Arnaud & West, Mike, 2004. "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 156-168, January.
  2. Marco J. Lombardi, 2004. "Bayesian inference for alpha-stable distributions: a random walk MCMC approach," Econometrics Working Papers Archive wp2004_11, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  3. Nicolas Chopin, 2000. "A Sequential Particle Filter Method for Static Models," Working Papers 2000-45, Centre de Recherche en Economie et Statistique.
  4. Tsionas, Efthymios G., 1998. "Monte Carlo inference in econometric models with symmetric stable disturbances," Journal of Econometrics, Elsevier, vol. 88(2), pages 365-401, November.
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Cited by:
  1. Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February.
  2. Lombardi, Marco J. & Sgherri, Silvia, 2007. "(Un)naturally low? Sequential Monte Carlo tracking of the US natural interest rate," Working Paper Series 0794, European Central Bank.

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