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On the Exact Discretization of a Continuous Time AR(1) Model driven by either Long Memory or Antipersistent Innovations: A Fractional Algebra Approach

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  • Simos Theodore

    (University of Ioannina)

Abstract

Exact discretization formulae are established for a first-order stochastic differential equation driven by a fractional noise of either long memory or antipersistent type. We assume that the underlying process is sampled at non-unit equispaced observational intervals. Using fractional algebra techniques the exact discretization formulae are derived in terms of confluent hypergeometric and incomplete gamma functions which admit infinite order series expansions.

Suggested Citation

  • Simos Theodore, 2012. "On the Exact Discretization of a Continuous Time AR(1) Model driven by either Long Memory or Antipersistent Innovations: A Fractional Algebra Approach," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-26, November.
    • Handle: RePEc:bpj:jtsmet:v:4:y:2012:i:2:n:5
    DOI: 10.1515/1941-1928.1145
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    References listed on IDEAS

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    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. 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.
    3. Phillips, Peter C.B., 2009. "Long memory and long run variation," Journal of Econometrics, Elsevier, vol. 151(2), pages 150-158, August.
    4. Joanne S. Ercolani, 2011. "On the asymptotic properties of a feasible estimator of the continuous time long memory parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 512-517, September.
    5. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    6. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212, Elsevier.
    7. Henghsiu Tsai & K. S. Chan, 2005. "Maximum likelihood estimation of linear continuous time long memory processes with discrete time data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 703-716, November.
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    Cited by:

    1. 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.

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