IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v174y2019icp78-83.html
   My bibliography  Save this article

Maximum likelihood estimation of a TVP-VAR

Author

Listed:
  • Moura, Guilherme V.
  • Noriller, Mateus R.

Abstract

This paper proposes the maximum likelihood estimation of a vector autoregression with drifting coefficients and multivariate stochastic volatility. The coefficients are assumed to follow heteroscedastic random walks and the volatility of the system is modeled as a Wishart process, increasing the flexibility in describing the behavior of stochastic covariances. Exploiting the conjugacy between Normal, Wishart and multivariate beta distributions, filtering formulas for tracking the latent states and expression for the likelihood function can be obtained in closed form.

Suggested Citation

  • Moura, Guilherme V. & Noriller, Mateus R., 2019. "Maximum likelihood estimation of a TVP-VAR," Economics Letters, Elsevier, vol. 174(C), pages 78-83.
    • Handle: RePEc:eee:ecolet:v:174:y:2019:i:c:p:78-83
    DOI: 10.1016/j.econlet.2018.10.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176518304452
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2018.10.032?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. Christiane Baumeister & Gert Peersman, 2013. "Time-Varying Effects of Oil Supply Shocks on the US Economy," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(4), pages 1-28, October.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. 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.
    4. 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.
    5. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    6. Jordi Galí & Luca Gambetti, 2015. "The Effects of Monetary Policy on Stock Market Bubbles: Some Evidence," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 233-257, January.
    7. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2010. "Inflation-Gap Persistence in the US," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 43-69, January.
    8. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    9. 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.
    10. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    11. Kim, Dukpa, 2014. "Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility," Economics Letters, Elsevier, vol. 123(3), pages 282-286.
    12. Haroon Mumtaz & Francesco Zanetti, 2015. "Labor Market Dynamics: A Time-Varying Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(3), pages 319-338, June.
    13. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    14. K. Triantafyllopoulos, 2011. "Time-varying vector autoregressive models with stochastic volatility," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 369-382, September.
    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. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    2. Roberto Leon-Gonzalez & Blessings Majoni, 2023. "Exact Likelihood for Inverse Gamma Stochastic Volatility Models," GRIPS Discussion Papers 23-07, National Graduate Institute for Policy Studies.
    3. Moura, Guilherme V. & Santos, André A. P., 2019. "Comparing Forecasts of Extremely Large Conditional Covariance Matrices," DES - Working Papers. Statistics and Econometrics. WS 29291, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Qiao, Xingzhi & Zhu, Huiming & Zhang, Zhongqingyang & Mao, Weifang, 2022. "Time-frequency transmission mechanism of EPU, investor sentiment and financial assets: A multiscale TVP-VAR connectedness analysis," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    5. Moura, Guilherme V. & Santos, André A.P. & Ruiz, Esther, 2020. "Comparing high-dimensional conditional covariance matrices: Implications for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 118(C).

    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. Joshua C.C. Chan & Rodney W. Strachan, 2023. "Bayesian State Space Models In Macroeconometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 58-75, February.
    2. Todd E. Clark & Francesco Ravazzolo, 2012. "The macroeconomic forecasting performance of autoregressive models with alternative specifications of time-varying volatility," Working Paper 2012/09, Norges Bank.
    3. 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.
    4. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    5. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    6. Belomestny, Denis & Krymova, Ekaterina & Polbin, Andrey, 2021. "Bayesian TVP-VARX models with time invariant long-run multipliers," Economic Modelling, Elsevier, vol. 101(C).
    7. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    8. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    9. Clark, Todd E. & Davig, Troy, 2011. "Decomposing the declining volatility of long-term inflation expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 981-999, July.
    10. 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.
    11. Dellaportas, Petros & Titsias, Michalis K. & Petrova, Katerina & Plataniotis, Anastasios, 2023. "Scalable inference for a full multivariate stochastic volatility model," Journal of Econometrics, Elsevier, vol. 232(2), pages 501-520.
    12. Denis Belomestny & Ekaterina Krymova & Andrey Polbin, 2020. "Estimating TVP-VAR models with time invariant long-run multipliers," Papers 2008.00718, arXiv.org.
    13. Petrova, Katerina, 2019. "A quasi-Bayesian local likelihood approach to time varying parameter VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 286-306.
    14. Mandalinci, Zeyyad, 2017. "Forecasting inflation in emerging markets: An evaluation of alternative models," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1082-1104.
    15. 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.
    16. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    17. Danilo Leiva-Leon & Luis Uzeda, 2023. "Endogenous Time Variation in Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 105(1), pages 125-142, January.
    18. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    19. Todd E. Clark & Stephen J. Terry, 2010. "Time Variation in the Inflation Passthrough of Energy Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1419-1433, October.
    20. Haque, Qazi & Magnusson, Leandro M., 2021. "Uncertainty shocks and inflation dynamics in the U.S," Economics Letters, Elsevier, vol. 202(C).

    More about this item

    Keywords

    Time-varying parameters VAR; Multivariate stochastic volatility; Wishart distribution; Maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:ecolet:v:174:y:2019:i:c:p:78-83. 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/ecolet .

    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.