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Extended Fractional Gaussian Noise and Simple ARFIMA Approximations

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  • Man Kasing

    (Western Illinois University)

Abstract

Extended fractional Gaussian noise (eFGN) is the limiting structure of long memory time series aggregates. We propose a flexible class of low-order ARFIMA (0, d, q) models that closely approximates eFGN. Such ARFIMA approximation and a metric to measure precision can be easily obtained from the eigenvector and eigenvalue of an aggregation matrix of dimension q+1, constructed by utilizing the invariant property. A comparison to Man and Tiao's (2006) ARFIMA (0, d, dI) approximation that uses fixed MA order is also made. In practice, our result suggests that when aggregated long enough, many long memory time series aggregates will tend to follow a low-order ARFIMA model with pretty stable MA structure determined by d. This makes simple ARFIMA models appealing for modeling long memory time series aggregates.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:jtsmet:v:2:y:2010:i:1:n:7
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    References listed on IDEAS

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    1. Man, K.S. & Tiao, G.C., 2006. "Aggregation effect and forecasting temporal aggregates of long memory processes," International Journal of Forecasting, Elsevier, vol. 22(2), pages 267-281.
    2. Man, K. S., 2003. "Long memory time series and short term forecasts," International Journal of Forecasting, Elsevier, vol. 19(3), pages 477-491.
    3. Souza, Leonardo R. & Smith, Jeremy, 2004. "Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study," International Journal of Forecasting, Elsevier, vol. 20(3), pages 487-502.
    4. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    5. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    6. 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.
    7. William Wei & Daniel Stram, 1988. "An eigenvalue approach to the limiting behavior of time series aggregates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, pages 101-110.
    8. 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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