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The Estimation of Continuous Parameter Long-Memory Time Series Models


  • Chambers, Marcus J.


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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    References listed on IDEAS

    1. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    2. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    4. Andrews, Donald W. K., 1991. "An empirical process central limit theorem for dependent non-identically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 187-203, August.
    5. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    6. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation for Research in Economics, Yale University.
    7. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
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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. 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.
    4. 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.
    5. 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.
    6. repec:hal:journl:peer-00815563 is not listed on IDEAS
    7. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    8. 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.
    9. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.

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