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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. Copyright 2009 Blackwell Publishing Ltd

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
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    References listed on IDEAS

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    5. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
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    11. 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.
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    Cited by:

    1. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    2. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    3. 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.
    4. Bensalma, Ahmed, 2018. "Two Distinct Seasonally Fractionally Differenced Periodic Processes," MPRA Paper 84969, University Library of Munich, Germany.
    5. 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.
    6. Gbaguidi, David Sedo, 2011. "Expectations Impact on the Effectiveness of the Inflation-Real Activity Trade-Off," MPRA Paper 35482, University Library of Munich, Germany.
    7. 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.
    8. 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.

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