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A Fast Fractional Difference Algorithm

Author

Listed:
  • Andreas Noack Jensen

    (University of Copenhagen)

  • Morten Ø. Nielsen

    (Queen's University and CREATES)

Abstract

We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T^2, where T is the length of the time series. Our algorithm allows calculation speed of order T log(T). For moderate and large sample sizes, the difference in computation time is substantial.

Suggested Citation

  • Andreas Noack Jensen & Morten Ø. Nielsen, 2013. "A Fast Fractional Difference Algorithm," Working Paper 1307, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1307
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1307.pdf
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    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. Bollerslev, Tim & Osterrieder, Daniela & Sizova, Natalia & Tauchen, George, 2013. "Risk and return: Long-run relations, fractional cointegration, and return predictability," Journal of Financial Economics, Elsevier, vol. 108(2), pages 409-424.
    3. 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.
    4. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Circular convolution theorem; fast Fourier transform; fractional difference;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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