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Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes

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  • HENGHSIU TSAI
  • K. S. CHAN

Abstract

. We study the autocorrelation structure of aggregates from a continuous‐time process. The underlying continuous‐time process or some of its higher derivative is assumed to be a stationary continuous‐time auto‐regressive fractionally integrated moving‐average (CARFIMA) process with Hurst parameter H. We derive closed‐form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. The limiting model of the aggregates, after appropriate number of differencing, is shown to be some functional of the standard fractional Brownian motion with the same Hurst parameter of the continuous‐time process from which the aggregates are measured. These results are then used to assess the loss of forecasting efficiency due to aggregation.

Suggested Citation

  • Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 583-597, December.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:4:p:583-597
    DOI: 10.1111/j.1467-9469.2005.00455.x
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    References listed on IDEAS

    as
    1. Henghsiu Tsai & K. S. Chan, 2005. "Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 691-713, September.
    2. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    3. Beran, Jan & Ocker, Dirk, 2000. "Temporal aggregation of stationary and nonstationary FARIMA (p, d, 0) models," CoFE Discussion Papers 00/22, University of Konstanz, Center of Finance and Econometrics (CoFE).
    4. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
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    Cited by:

    1. Man Kasing, 2010. "Extended Fractional Gaussian Noise and Simple ARFIMA Approximations," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-26, September.
    2. repec:hal:journl:peer-00815563 is not listed on IDEAS
    3. Theodore Simos & Mike Tsionas, 2018. "Bayesian inference of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme," Computational Statistics, Springer, vol. 33(4), pages 1687-1713, December.
    4. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
    5. Michael A. Thornton & Marcus J. Chambers, 2013. "Continuous-time autoregressive moving average processes in discrete time: representation and embeddability," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 552-561, September.

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