On-line Bayesian estimation of AR signals in symmetric alpha-stable noise
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.
|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|
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- Nicolas Chopin, 2000.
"A Sequential Particle Filter Method for Static Models,"
2000-45, Centre de Recherche en Economie et Statistique.
- Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
- 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.
- 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".
- 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.
- 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.
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