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Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility

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  • Kim, Dukpa

Abstract

This paper analyzes the maximum likelihood estimation for vector autoregressions with stochastic volatility. The stochastic volatility is modeled following Uhlig (1997). The asymptotic distribution of the maximum likelihood estimate is discussed under mild regularity conditions. The maximum likelihood estimate can be obtained via an iterative method. In that case, the maximum likelihood estimate becomes the iteratively reweighted least squares estimate analyzed in Rubin (1983). The iteratively reweighted least squares estimate is computationally much simpler than the Bayesian method offered by Uhlig (1997).

Suggested Citation

  • Kim, Dukpa, 2014. "Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility," Economics Letters, Elsevier, vol. 123(3), pages 282-286.
    • Handle: RePEc:eee:ecolet:v:123:y:2014:i:3:p:282-286
    DOI: 10.1016/j.econlet.2014.03.004
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    References listed on IDEAS

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    1. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    2. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    3. 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.
    4. 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.
    5. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    6. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
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    Cited by:

    1. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 15(2), pages 247-285.
    2. Moura, Guilherme V. & Noriller, Mateus R., 2019. "Maximum likelihood estimation of a TVP-VAR," Economics Letters, Elsevier, vol. 174(C), pages 78-83.
    3. 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.
    4. Amendola, Alessandra & Braione, Manuela & Candila, Vincenzo & Storti, Giuseppe, 2020. "A Model Confidence Set approach to the combination of multivariate volatility forecasts," International Journal of Forecasting, Elsevier, vol. 36(3), pages 873-891.
    5. Xinyu Huang & Weihao Han & David Newton & Emmanouil Platanakis & Dimitrios Stafylas & Charles Sutcliffe, 2023. "The diversification benefits of cryptocurrency asset categories and estimation risk: pre and post Covid-19," The European Journal of Finance, Taylor & Francis Journals, vol. 29(7), pages 800-825, May.
    6. Roberto Leon‐Gonzalez & Blessings Majoni, 2025. "Exact likelihood for inverse gamma stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 46(4), pages 774-795, July.
    7. Moura, Guilherme V. & Santos, André A. P. & Ruiz Ortega, Esther, 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.
    8. 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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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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