IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v32y2024icp98-121.html
   My bibliography  Save this article

Spectral Subsampling MCMC for Stationary Multivariate Time Series with Applications to Vector ARTFIMA Processes

Author

Listed:
  • Villani, Mattias
  • Quiroz, Matias
  • Kohn, Robert
  • Salomone, Robert

Abstract

A multivariate generalisation of the Whittle likelihood is used to extend spectral subsampling MCMC to stationary multivariate time series by subsampling matrix-valued periodogram observations in the frequency domain. To assess the performance of the methodology in challenging problems, a multivariate generalisation of the autoregressive tempered fractionally integrated moving average model (ARTFIMA) is introduced and some of its properties derived. Bayesian inference based on the Whittle likelihood is demonstrated to be a fast and accurate alternative to the exact time domain likelihood. Spectral subsampling is shown to provide up to two orders of magnitude additional speed-up, while retaining MCMC sampling efficiency and accuracy, compared to spectral methods using the full dataset.

Suggested Citation

  • Villani, Mattias & Quiroz, Matias & Kohn, Robert & Salomone, Robert, 2024. "Spectral Subsampling MCMC for Stationary Multivariate Time Series with Applications to Vector ARTFIMA Processes," Econometrics and Statistics, Elsevier, vol. 32(C), pages 98-121.
    • Handle: RePEc:eee:ecosta:v:32:y:2024:i:c:p:98-121
    DOI: 10.1016/j.ecosta.2022.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S245230622200106X
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2022.10.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    3. Matias Quiroz & Robert Kohn & Mattias Villani & Minh-Ngoc Tran, 2019. "Speeding Up MCMC by Efficient Data Subsampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 831-843, April.
    4. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).
    5. Matias Quiroz & Mattias Villani & Robert Kohn & Minh-Ngoc Tran & Khue-Dung Dang, 2018. "Subsampling MCMC - an Introduction for the Survey Statistician," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 33-69, December.
    6. Timothy F. Welch & Alyas Widita, 2019. "Big data in public transportation: a review of sources and methods," Transport Reviews, Taylor & Francis Journals, vol. 39(6), pages 795-818, November.
    7. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    8. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    9. George Deligiannidis & Arnaud Doucet & Michael K. Pitt, 2018. "The correlated pseudomarginal method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 839-870, November.
    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. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    2. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    4. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    6. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    7. Matias Quiroz & Mattias Villani & Robert Kohn & Minh-Ngoc Tran & Khue-Dung Dang, 2018. "Subsampling MCMC - an Introduction for the Survey Statistician," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 33-69, December.
    8. Patrick Leung & Catherine S. Forbes & Gael M Martin & Brendan McCabe, 2019. "Forecasting Observables with Particle Filters: Any Filter Will Do!," Monash Econometrics and Business Statistics Working Papers 22/19, Monash University, Department of Econometrics and Business Statistics.
    9. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    10. Loaiza-Maya, Rubén & Nibbering, Didier & Zhu, Dan, 2024. "Hybrid unadjusted Langevin methods for high-dimensional latent variable models," Journal of Econometrics, Elsevier, vol. 241(2).
    11. Golightly, Andrew & Bradley, Emma & Lowe, Tom & Gillespie, Colin S., 2019. "Correlated pseudo-marginal schemes for time-discretised stochastic kinetic models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 92-107.
    12. Wiqvist, Samuel & Golightly, Andrew & McLean, Ashleigh T. & Picchini, Umberto, 2021. "Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    13. Quiroz, Matias & Villani, Mattias & Kohn, Robert, 2015. "Scalable Mcmc For Large Data Problems Using Data Subsampling And The Difference Estimator," Working Paper Series 306, Sveriges Riksbank (Central Bank of Sweden).
    14. Phillip, Andrew & Chan, Jennifer & Peiris, Shelton, 2020. "On generalized bivariate student-t Gegenbauer long memory stochastic volatility models with leverage: Bayesian forecasting of cryptocurrencies with a focus on Bitcoin," Econometrics and Statistics, Elsevier, vol. 16(C), pages 69-90.
    15. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    16. Pratiti Chatterjee & David Gunawan & Robert Kohn, 2020. "The Interaction Between Credit Constraints and Uncertainty Shocks," Papers 2004.14719, arXiv.org.
    17. 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).
    18. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    19. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    20. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.

    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:eee:ecosta:v:32:y:2024:i:c:p:98-121. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.