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Computationally efficient methods for two multivariate fractionally integrated models

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  • Rebecca J. Sela
  • Clifford M. Hurvich
Abstract
. We discuss two distinct multivariate time‐series models that extend the univariate ARFIMA (autoregressive fractionally integrated moving average) model. We discuss the different implications of the two models and describe an extension to fractional cointegration. We describe algorithms for computing the covariances of each model, for computing the quadratic form and approximating the determinant for maximum likelihood estimation and for simulating from each model. We compare the speed and accuracy of each algorithm with existing methods individually. Then, we measure the performance of the maximum likelihood estimator and of existing methods in a Monte Carlo. These algorithms are much more computationally efficient than the existing algorithms and are equally accurate, making it feasible to model multivariate long memory time series and to simulate from these models. We use maximum likelihood to fit models to data on goods and services inflation in the United States.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:6:p:631-651
    DOI: 10.1111/j.1467-9892.2009.00631.x
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    References listed on IDEAS

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    11. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
    12. Chen, Willa W. & Hurvich, Clifford M. & Lu, Yi, 2006. "On the Correlation Matrix of the Discrete Fourier Transform and the Fast Solution of Large Toeplitz Systems for Long-Memory Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 812-822, June.
    13. Pai, Jeffrey & Ravishanker, Nalini, 2009. "A multivariate preconditioned conjugate gradient approach for maximum likelihood estimation in vector long memory processes," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1282-1289, May.
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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. Do, Hung Xuan & Nepal, Rabindra & Jamasb, Tooraj, 2020. "Electricity market integration, decarbonisation and security of supply: Dynamic volatility connectedness in the Irish and Great Britain markets," Energy Economics, Elsevier, vol. 92(C).
    3. Yao Axel Ehouman, 2019. "Volatility transmission between oil prices and banks stock prices as a new source of instability: Lessons from the US Experience," Working Papers hal-04141868, HAL.
    4. G. Mesters & S. J. Koopman & M. Ooms, 2016. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 659-687, April.
    5. Gbaguidi DAVID, 2011. "Expectations Impact On The Effectiveness Of The Inflation-Real Activity Trade-Off," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 2(2), pages 141-181.
    6. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    7. Stefanos Kechagias & Vladas Pipiras, 2020. "Modeling bivariate long‐range dependence with general phase," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 268-292, March.
    8. Marina Balboa & Paulo M. M. Rodrigues & Antonio Rubia & A. M. Robert Taylor, 2021. "Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 544-565, August.
    9. Yao Axel Ehouman, 2019. "Volatility transmission between oil prices and banks stock prices as a new source of instability: Lessons from the US Experience," EconomiX Working Papers 2019-19, University of Paris Nanterre, EconomiX.
    10. Ross Doppelt & Keith O'Hara, 2018. "Bayesian Estimation of Fractionally Integrated Vector Autoregressions and an Application to Identified Technology Shocks," 2018 Meeting Papers 1212, Society for Economic Dynamics.
    11. Ehouman, Yao Axel, 2020. "Volatility transmission between oil prices and banks' stock prices as a new source of instability: Lessons from the United States experience," Economic Modelling, Elsevier, vol. 91(C), pages 198-217.
    12. 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.
    13. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    14. Yao Axel Ehouman, 2020. "Volatility transmission between oil prices and banks’ stock prices as a new source of instability: Lessons from the United States experience," Post-Print hal-02960571, HAL.
    15. Do, Hung Xuan & Brooks, Robert & Treepongkaruna, Sirimon & Wu, Eliza, 2016. "Stock and currency market linkages: New evidence from realized spillovers in higher moments," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 167-185.
    16. Bensalma, Ahmed, 2018. "Two Distinct Seasonally Fractionally Differenced Periodic Processes," MPRA Paper 84969, University Library of Munich, Germany.
    17. Gbaguidi, David, 2012. "La courbe de Phillips : temps d’arbitrage et/ou arbitrage de temps," L'Actualité Economique, Société Canadienne de Science Economique, vol. 88(1), pages 87-119, mars.

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