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A Class of Antipersistent Processes

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  • Pascal Bondon
  • Wilfredo Palma

Abstract

. We introduce a class of stationary processes characterized by the behaviour of their infinite moving average parameters. We establish the asymptotic behaviour of the covariance function and the behaviour around zero of the spectral density of these processes, showing their antipersistent character. Then, we discuss the existence of an infinite autoregressive representation for this family of processes, and we present some consequences for fractional autoregressive moving average models.

Suggested Citation

  • Pascal Bondon & Wilfredo Palma, 2007. "A Class of Antipersistent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 261-273, March.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:2:p:261-273
    DOI: 10.1111/j.1467-9892.2006.00509.x
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    Cited by:

    1. Hailin Sang & Yongli Sang, 2017. "Memory properties of transformations of linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 79-103, April.
    2. Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CIRJE F-Series CIRJE-F-608, CIRJE, Faculty of Economics, University of Tokyo.
    3. Lopes, Sílvia R.C. & Prass, Taiane S., 2014. "Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 278-307.
    4. Hassler, Uwe, 2012. "Impulse responses of antipersistent processes," Economics Letters, Elsevier, vol. 116(3), pages 454-456.
    5. Zevallos, Mauricio & Palma, Wilfredo, 2013. "Minimum distance estimation of ARFIMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 242-256.
    6. Shelton Peiris & Richard Hunt, 2023. "Revisiting the Autocorrelation of Long Memory Time Series Models," Mathematics, MDPI, vol. 11(4), pages 1-8, February.

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