IDEAS home Printed from https://ideas.repec.org/p/ven/wpaper/201319.html
   My bibliography  Save this paper

Adaptive Sticky Generalized Metropolis

Author

Listed:
  • Fabrizio Leisen

    (University of Kent)

  • Roberto Casarin

    (University of Venice C� Foscari)

  • David Luengo

    (Universidad Politecnica de Madrid)

  • Luca Martino

    (Universidad Carlos III de Madrid)

Abstract

We introduce a new class of adaptive Metropolis algorithms called adaptive sticky algorithms for efficient general-purpose simulation from a target probability distribution. The transition of the Metropolis chain is based on a multiple-try scheme and the different proposals are generated by adaptive nonparametric distributions. Our adaptation strategy uses the interpolation of support points from the past history of the chain as in the adaptive rejection Metropolis. The algorithm efficiency is strengthened by a step that controls the evolution of the set of support points. This extra stage improves the computational cost and accelerates the convergence of the proposal distribution to the target. Despite the algorithms are presented for univariate target distributions, we show that they can be easily extended to the multivariate context by a Gibbs sampling strategy. We show the ergodicity of the proposed algorithms and illustrate their efficiency and effectiveness through some simulated examples involving target distributions with complex structures.

Suggested Citation

  • Fabrizio Leisen & Roberto Casarin & David Luengo & Luca Martino, 2013. "Adaptive Sticky Generalized Metropolis," Working Papers 2013:19, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2013:19
    as

    Download full text from publisher

    File URL: http://www.unive.it/pag/fileadmin/user_upload/dipartimenti/economia/doc/Pubblicazioni_scientifiche/working_papers/2013/WP_DSE_casarin_leisen_luengo_martino_19_13.pdf
    File Function: First version, anno
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    3. Casarin, Roberto & Craiu, Radu & Leisen, Fabrizio, 2011. "Interacting multiple -- Try algorithms with different proposal distributions," DES - Working Papers. Statistics and Econometrics. WS ws110402, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. repec:dau:papers:123456789/6072 is not listed on IDEAS
    5. Luca Martino & Jesse Read, 2013. "On the flexibility of the design of multiple try Metropolis schemes," Computational Statistics, Springer, vol. 28(6), pages 2797-2823, December.
    6. Craiu, Radu V. & Rosenthal, Jeffrey & Yang, Chao, 2009. "Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1454-1466.
    7. Martino, Luca & Del Olmo, Victor Pascual & Read, Jesse, 2012. "A multi-point Metropolis scheme with generic weight functions," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1445-1453.
    8. Ajay Jasra & David A. Stephens & Christopher C. Holmes, 2007. "Population-Based Reversible Jump Markov Chain Monte Carlo," Biometrika, Biometrika Trust, vol. 94(4), pages 787-807.
    9. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    10. Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2012. "A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation," Journal of Econometrics, Elsevier, vol. 171(2), pages 101-120.
    11. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    12. Campillo, Fabien & Rakotozafy, Rivo & Rossi, Vivien, 2009. "Parallel and interacting Markov chain Monte Carlo algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3424-3433.
    13. Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
    14. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

    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. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524.
    2. Deschamps, P., 2015. "Alternative Formulation of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors," LIDAM Discussion Papers CORE 2015020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Hsieh, Ping-Hung & Yang, J. Jimmy, 2009. "A censored stochastic volatility approach to the estimation of price limit moves," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 337-351, March.
    4. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    5. 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.
    6. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    7. Du, Xiaodong & Yu, Cindy L. & Hayes, Dermot J., 2011. "Speculation and volatility spillover in the crude oil and agricultural commodity markets: A Bayesian analysis," Energy Economics, Elsevier, vol. 33(3), pages 497-503, May.
    8. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    9. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.
    10. Asai, Manabu, 2009. "Bayesian analysis of stochastic volatility models with mixture-of-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2579-2596.
    11. Carlos A. Abanto‐Valle & Helio S. Migon & Hedibert F. Lopes, 2010. "Bayesian modeling of financial returns: A relationship between volatility and trading volume," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 172-193, March.
    12. Antonello Loddo & Shawn Ni & Dongchu Sun, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 342-355, July.
    13. Jensen, Mark J. & Maheu, John M., 2014. "Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture," Journal of Econometrics, Elsevier, vol. 178(P3), pages 523-538.
    14. Sujay K Mukhoti, "undated". "Dynamic Feedback Effect And Skewness In Non-Stationary Stochastic Volatility Model With Leverage," Working papers 145, Indian Institute of Management Kozhikode.
    15. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    16. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    17. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    18. Aycan HEPSAG, 2016. "Asymmetric stochastic volatility in central and eastern European stock markets," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(2(607), S), pages 135-144, Summer.
    19. António A. F. Santos, 2015. "On the Forecasting of Financial Volatility Using Ultra-High Frequency Data," GEMF Working Papers 2015-17, GEMF, Faculty of Economics, University of Coimbra.
    20. Shota Gugushvili & Frank van der Meulen & Moritz Schauer & Peter Spreij, 2018. "Nonparametric Bayesian volatility estimation," Papers 1801.09956, arXiv.org, revised Mar 2019.

    More about this item

    Keywords

    Adaptive Markov chain Monte Carlo; Adaptive rejection Metropolis; Muliple-try Metropolis; Metropolis within Gibbs.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:ven:wpaper:2013:19. 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: Geraldine Ludbrook (email available below). General contact details of provider: https://edirc.repec.org/data/dsvenit.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.