IDEAS home Printed from https://ideas.repec.org/p/fir/econom/wp2004_05.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • Marco J. Lombardi & Simon J. Godsill, 2004. "On-line Bayesian estimation of AR signals in symmetric alpha-stable noise," Econometrics Working Papers Archive wp2004_05, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:wp2004_05
    as

    Download full text from publisher

    File URL: https://labdisia.disia.unifi.it/ricerca/pubblicazioni/working_papers/2004/wp2004_05.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3743-3756.
    2. 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.
    3. Lombardi, Marco J. & Sgherri, Silvia, 2007. "(Un)naturally low? Sequential Monte Carlo tracking of the US natural interest rate," Working Paper Series 794, European Central Bank.
    4. Lombardi, Marco J. & Sgherri, Silvia, 2007. "(Un)naturally low? Sequential Monte Carlo tracking of the US natural interest rate," Working Paper Series 794, European Central Bank.
    5. Saikat Saha, 2015. "Noise Robust Online Inference for Linear Dynamic Systems," Papers 1504.05723, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    2. Nicolas Chopin, 2007. "Dynamic Detection of Change Points in Long Time Series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 349-366, June.
    3. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    4. repec:wyi:journl:002173 is not listed on IDEAS
    5. Ioannis Bournakis & Mike Tsionas, 2024. "A Non‐parametric Estimation of Productivity with Idiosyncratic and Aggregate Shocks: The Role of Research and Development (R&D) and Corporate Tax," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 641-671, June.
    6. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    7. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    8. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    9. Jeong Eun Lee & Christian Robert, 2013. "Imortance Sampling Schemes for Evidence Approximation in Mixture Models," Working Papers 2013-42, Center for Research in Economics and Statistics.
    10. James Martin & Ajay Jasra & Emma McCoy, 2013. "Inference for a class of partially observed point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 413-437, June.
    11. Lange, Rutger-Jan, 2024. "Bellman filtering and smoothing for state–space models," Journal of Econometrics, Elsevier, vol. 238(2).
    12. Nathaniel Tomasetti & Catherine Forbes & Anastasios Panagiotelis, 2019. "Updating Variational Bayes: Fast Sequential Posterior Inference," Monash Econometrics and Business Statistics Working Papers 13/19, Monash University, Department of Econometrics and Business Statistics.
    13. Strid, Ingvar, 2010. "Efficient parallelisation of Metropolis-Hastings algorithms using a prefetching approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2814-2835, November.
    14. Carlos Carvalho & Stefano Eusepi & Emanuel Moench & Bruce Preston, 2023. "Anchored Inflation Expectations," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 1-47, January.
    15. Sampaio, Jhames M. & Morettin, Pedro A., 2020. "Stable Randomized Generalized Autoregressive Conditional Heteroskedastic Models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 67-83.
    16. Ho, Paul, 2023. "Global robust Bayesian analysis in large models," Journal of Econometrics, Elsevier, vol. 235(2), pages 608-642.
    17. 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.
    18. Emmanuel Mamatzakis & Mike G. Tsionas, 2021. "Testing for persistence in US mutual funds’ performance: a Bayesian dynamic panel model," Annals of Operations Research, Springer, vol. 299(1), pages 1203-1233, April.
    19. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.
    20. Mariolis Theodore & Konstantakis Konstantinos N. & Michaelides Panayotis G. & Tsionas Efthymios G., 2019. "A non-linear Keynesian Goodwin-type endogenous model of the cycle: Bayesian evidence for the USA," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(1), pages 1-16, February.
    21. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2008. "How Structural Are Structural Parameters?," NBER Chapters, in: NBER Macroeconomics Annual 2007, Volume 22, pages 83-137, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    Particle filters; Kalman filter; Alpha-stable distributions; Scale mixture of normals.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fir:econom:wp2004_05. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fabrizio Cipollini (email available below). General contact details of provider: https://edirc.repec.org/data/dsfirit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.