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The Estimation of Continuous Parameter Long-Memory Time Series Models

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  • Chambers, Marcus J.

Abstract

A class of univariate fractional ARIMA models with a continuous time parameter is developed for the purpose of modeling long-memory time series. The spectral density of discretely observed data is derived for both point observations (stock variables) and integral observations (flow variables). A frequency domain maximum likelihood method is proposed for estimating the longmemory parameter and is shown to be consistent and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.

Suggested Citation

  • Chambers, Marcus J., 1996. "The Estimation of Continuous Parameter Long-Memory Time Series Models," Econometric Theory, Cambridge University Press, vol. 12(02), pages 374-390, June.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:02:p:374-390_00
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    Cited by:

    1. Theodore Simos, 2008. "The exact discrete model of a system of linear stochastic differential equations driven by fractional noise," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1019-1031, November.
    2. Hwang, Soosung, 2000. "The Effects Of Systematic Sampling And Temporal Aggregation On Discrete Time Long Memory Processes And Their Finite Sample Properties," Econometric Theory, Cambridge University Press, vol. 16(03), pages 347-372, June.
    3. Leonenko, Nikolai N. & Sharapov, Michail M. & El-Bassiouny, Ahmed H., 2000. "On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 121-130, June.
    4. repec:hal:journl:peer-00815563 is not listed on IDEAS
    5. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, vol. 18(2), pages 299-313.
    6. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    7. Joanne S. Ercolani, 2010. "On the Asymptotic Properties of a Feasible Estimator of the Continuous Time Long Memory Parameter," Discussion Papers 10-09, Department of Economics, University of Birmingham.
    8. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    9. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.

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