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Maximum likelihood estimation of a TVP-VAR

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    5. 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.
    6. 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.
    7. 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.
    8. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Kim, Dukpa, 2014. "Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility," Economics Letters, Elsevier, vol. 123(3), pages 282-286.
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    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).

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    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

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