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The exact discrete model of a system of linear stochastic differential equations driven by fractional noise

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  • Theodore Simos

Abstract

. This paper derives the exact discrete model (EDM) of a kth‐order system of stochastic differential equations driven by a vector fractional noise under fixed initial conditions. The EDM can be used for the Gaussian estimation and forecasting with long‐memory discrete‐time equispaced data. Detailed formulae which are necessary for the construction and numerical evaluation of the Gaussian likelihood under two observation schemes are established. State variables can be observed either at equispaced points in time or as integrals over the observational interval.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:1019-1031
    DOI: 10.1111/j.1467-9892.2008.00593.x
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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.
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    3. Bergstrom, A.R., 1997. "Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 13(4), pages 467-505, February.
    4. Chambers, Marcus J., 1996. "The Estimation of Continuous Parameter Long-Memory Time Series Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 374-390, June.
    5. Robinson, P M, 1988. "Using Gaussian Estimators Robustly," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(1), pages 97-106, February.
    6. Bergstrom, A. R., 1985. "The Estimation of Parameters in Nonstationary Higher Order Continuous-Time Dynamic Models," Econometric Theory, Cambridge University Press, vol. 1(3), pages 369-385, December.
    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.
    8. Chambers, Marcus J., 1999. "Discrete time representation of stationary and non-stationary continuous time systems," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 619-639, February.
    9. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-152, January.
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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.
    2. 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.

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