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Second-order continuous-time non-stationary Gaussian autoregression

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  • N. Lin
  • S. Lototsky

Abstract

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven by Gaussian white noise. The emphasis is on the non-ergodic case, when the roots of the corresponding characteristic equation are not both in the left half-plane. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • N. Lin & S. Lototsky, 2014. "Second-order continuous-time non-stationary Gaussian autoregression," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 19-49, April.
    • Handle: RePEc:spr:sistpr:v:17:y:2014:i:1:p:19-49
    DOI: 10.1007/s11203-014-9090-9
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    References listed on IDEAS

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    1. Greenwood, P. E. & Wefelmeyer, W., 1993. "Asymptotic minimax results for stochastic process families with critical points," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 107-116, January.
    2. Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
    3. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
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    Cited by:

    1. Ana Prior & Marina Kleptsyna & Paula Milheiro-Oliveira, 2017. "On maximum likelihood estimation of the drift matrix of a degenerated O–U process," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 57-78, April.

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