IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v181y2023ics0167947323000014.html
   My bibliography  Save this article

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Author

Listed:
  • Sui, Yuelei
  • Holan, Scott H.
  • Yang, Wen-Hsi

Abstract

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. To address this issue, a computationally efficient multivariate Bayesian Circular Lattice Filter is developed, extending the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The proposed estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of the proposed approach, a comprehensive comparison with other competing methods is conducted through simulation studies and finds that, in most cases, the proposed approach performs superior in terms of the average squared error between the estimated and true time-varying spectral density. Finally, the methodology is demonstrated through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.

Suggested Citation

  • Sui, Yuelei & Holan, Scott H. & Yang, Wen-Hsi, 2023. "Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:csdana:v:181:y:2023:i:c:s0167947323000014
    DOI: 10.1016/j.csda.2023.107690
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323000014
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107690?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. Wenjie Zhao & Raquel Prado, 2020. "Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 759-784, November.
    2. Zoey Yi Zhao & Meng Xie & Mike West, 2016. "Dynamic dependence networks: Financial time series forecasting and portfolio decisions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(3), pages 311-332, May.
    3. Jouchi Nakajima & Mike West, 2013. "Bayesian Analysis of Latent Threshold Dynamic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 151-164, April.
    4. Nakajima, Jouchi & Kasuya, Munehisa & Watanabe, Toshiaki, 2011. "Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 225-245, September.
    5. Ombao H. C & Raz J. A & von Sachs R. & Malow B. A, 2001. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 543-560, June.
    6. Zoey Zhao & Meng Xie & Mike West, 2016. "Rejoinder to ‘Dynamic dependence networks: Financial time series forecasting and portfolio decisions’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(3), pages 336-339, May.
    7. Daniel R. Kowal & David S. Matteson & David Ruppert, 2017. "A Bayesian Multivariate Functional Dynamic Linear Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 733-744, April.
    8. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    9. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    10. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    11. K. Triantafyllopoulos, 2007. "Covariance estimation for multivariate conditionally Gaussian dynamic linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 551-569.
    12. Huerta, Gabriel & Lopes, Hedibert Freitas, 2000. "Bayesian forecasting and inference in latent structure for the Brazilian Industrial Production Index," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(1), May.
    13. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    14. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    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. Bruno P. C. Levy & Hedibert F. Lopes, 2021. "Dynamic Ordering Learning in Multivariate Forecasting," Papers 2101.04164, arXiv.org, revised Nov 2021.
    2. Kenichiro McAlinn, 2021. "Mixed‐frequency Bayesian predictive synthesis for economic nowcasting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1143-1163, November.
    3. Lopes, Hedibert F. & McCulloch, Robert E. & Tsay, Ruey S., 2022. "Parsimony inducing priors for large scale state–space models," Journal of Econometrics, Elsevier, vol. 230(1), pages 39-61.
    4. McAlinn, Kenichiro & West, Mike, 2019. "Dynamic Bayesian predictive synthesis in time series forecasting," Journal of Econometrics, Elsevier, vol. 210(1), pages 155-169.
    5. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
    6. Jouchi Nakajima, 2011. "Time-Varying Parameter VAR Model with Stochastic Volatility: An Overview of Methodology and Empirical Applications," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 29, pages 107-142, November.
    7. Liu, Dayu & Xu, Ning & Zhao, Tingting & Song, Yang, 2018. "Identifying the nonlinear correlation between business cycle and monetary policy rule: Evidence from China and the U.S," Economic Modelling, Elsevier, vol. 73(C), pages 45-54.
    8. Hartwig, Benny, 2020. "Robust inference intime-varying structural VAR models: The DC-Cholesky multivariate stochasticvolatility model," Discussion Papers 34/2020, Deutsche Bundesbank.
    9. Rodríguez, Gabriel & Vassallo, Renato & Castillo B., Paul, 2023. "Effects of external shocks on macroeconomic fluctuations in Pacific Alliance countries," Economic Modelling, Elsevier, vol. 124(C).
    10. Juan Manuel Julio-Román & Fredy Gamboa-Estrada, 2019. "The Exchange Rate and Oil Prices in Colombia: A High Frequency Analysis," Borradores de Economia 1091, Banco de la Republica de Colombia.
    11. Zhaosu MENG & Wei WEI & Xiaotong LIU & Kedong YIN, 2018. "The Influence of International Capital Flow on the Effectiveness of Chinese Monetary Policy," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 21-40, December.
    12. Michaelis, Henrike & Watzka, Sebastian, 2017. "Are there differences in the effectiveness of quantitative easing at the zero-lower-bound in Japan over time?," Journal of International Money and Finance, Elsevier, vol. 70(C), pages 204-233.
    13. Sun, Weihong & Liu, Ding, 2023. "Great moderation with Chinese characteristics: Uncovering the role of monetary policy," Economic Modelling, Elsevier, vol. 121(C).
    14. Hernán Rincón-Castro & Pedro Rubiano-López & Lisseth Yaya-Garzón & Héctor M. Zárate-Solano, 2021. "Traspaso de la tasa de cambio a la inflación básica en Colombia: un análisis de parámetros cambiantes en el tiempo," Borradores de Economia 1177, Banco de la Republica de Colombia.
    15. Kim, Soohyeon & Kim, Jihyo & Heo, Eunnyeong, 2021. "Speculative incentives to hoard aluminum: Relationship between capital gains and inventories," Resources Policy, Elsevier, vol. 70(C).
    16. Daniele Bianchi & Kenichiro McAlinn, 2018. "Large-Scale Dynamic Predictive Regressions," Papers 1803.06738, arXiv.org.
    17. Michaelis, Henrike & Watzka, Sebastian, 2014. "Are there Differences in the Effectiveness of Quantitative Easing in Japan over Time?," Discussion Papers in Economics 21087, University of Munich, Department of Economics.
    18. Julio-Román, Juan Manuel, 2019. "Estimating the Exchange Rate Pass-Through: A Time-Varying Vector Auto-Regression with Residual Stochastic Volatility Approach," Working papers 21, Red Investigadores de Economía.
    19. Iiboshi, Hirokuni & Iwata, Yasuharu & Kajita, Yuto & Soma, Naoto, 2019. "Time-varying Fiscal Multipliers Identified by Systematic Component: A Bayesian Approach to TVP-SVAR model," MPRA Paper 92631, University Library of Munich, Germany.
    20. Tatsuki Okamoto & Yoichi Matsubayashi, 2017. "Empirical Evidence from a Japanese Lending Survey within the TVP-VAR Framework: Does the Credit Channel Matter for Monetary Policy?," Discussion Papers 1709, Graduate School of Economics, Kobe University.

    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:csdana:v:181:y:2023:i:c:s0167947323000014. 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: http://www.elsevier.com/locate/csda .

    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.