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Maximum Likelihood Estimation of VARMA Models Using a State-Space EM Algorithm

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  • Konstantinos Metaxoglou
  • Aaron Smith

Abstract

We introduce a state-space representation for vector autoregressive moving-average models that enables maximum likelihood estimation using the EM algorithm. We obtain closed-form expressions for both the E- and M-steps; the former requires the Kalman filter and a fixed-interval smoother, and the latter requires least squares-type regression. We show via simulations that our algorithm converges reliably to the maximum, whereas gradient-based methods often fail because of the highly nonlinear nature of the likelihood function. Moreover, our algorithm converges in a smaller number of function evaluations than commonly used direct-search routines. Overall, our approach achieves its largest performance gains when applied to models of high dimension. We illustrate our technique by estimating a high-dimensional vector moving-average model for an efficiency test of California's wholesale electricity market. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Suggested Citation

  • Konstantinos Metaxoglou & Aaron Smith, 2007. "Maximum Likelihood Estimation of VARMA Models Using a State-Space EM Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 666-685, September.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:5:p:666-685
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    Citations

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    Cited by:

    1. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2016. "Large Bayesian VARMAs," Journal of Econometrics, Elsevier, vol. 192(2), pages 374-390.
    2. 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.
    3. Francesca Di Iorio & Umberto Triacca, 2014. "Testing for A Set of Linear Restrictions in VARMA Models Using Autoregressive Metric: An Application to Granger Causality Test," Econometrics, MDPI, Open Access Journal, vol. 2(4), pages 1-14, December.
    4. Dufour, Jean-Marie & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
    5. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    6. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2014. "Large Bayesian VARMAs," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-06, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Joshua C.C. Chan & Eric Eisenstat, 2013. "Gibbs Samplers for VARMA and Its Extensions," ANU Working Papers in Economics and Econometrics 2013-604, Australian National University, College of Business and Economics, School of Economics.

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