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Maximum Likelihood Estimation of Stationary Multivariate ARFIMA Processes



This paper considers the maximum likelihood estimation of a class of stationary and invertible vector autoregressive fractionally integrated moving-average (VARFIMA) processes considered in Luceno (1996). The coverage of this class of VARFIMA processes is quite general and includes the model considered in Andersen et al. (2003) for describing the behavior of realized volatility as one of its special case. We suggest an conditional likelihood Durbin-Levsinson (CLDL) algorithm which employs the multivariate Durbin-Levinson algorithm of Whittle (1963) to efficiently evaluate the conditional likelihood function of the VARFIMA processes exactly. The computational cost of implementing this algorithm is much lower than that proposed in Sowell (1989), thus allowing us to conduct a Monte Carlo experiment to investigate the finite sample performance of the CLDL algorithm for 3-dimensional VARFIMA processes under the moderate sample size up to 400. The simulation results are very satisfactory and reveal the great potential of using our method for characterizing the realized volatility in Andersen et al. (2003) and the spatial data studied in Haslett and Raftery (1989).

Suggested Citation

  • Wen-Jen Tsay, 2007. "Maximum Likelihood Estimation of Stationary Multivariate ARFIMA Processes," IEAS Working Paper : academic research 07-A011, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  • Handle: RePEc:sin:wpaper:07-a011

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    Cited by:

    1. Kristoufek, Ladislav, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6484-6493.
    2. Rebecca J. Sela & Clifford M. Hurvich, 2009. "Computationally efficient methods for two multivariate fractionally integrated models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 631-651, November.
    3. Kristoufek, Ladislav, 2015. "On the interplay between short and long term memory in the power-law cross-correlations setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 218-222.
    4. Pai, Jeffrey & Ravishanker, Nalini, 2009. "Maximum likelihood estimation in vector long memory processes via EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4133-4142, October.

    More about this item


    Durbin-Levinson algorithm; Long memory; Maximum likelihood estimation; Multivariate time series;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • 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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