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Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency

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  • Gao, Jiti
  • Anh, Vo
  • Heyde, Chris
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Abstract

This paper considers statistical inference for nonstationary Gaussian processes with long-range dependence and intermittency. The existence of such a process has been established by Anh et al. (J. Statist. Plann. Inference 80 (1999) 95-110). We systematically consider the case where the spectral density of nonstationary Gaussian processes with stationary increments is of a general and flexible form. The spectral density function of fRBm is thus a special case of this general form. A continuous version of the Gauss-Whittle objective function is proposed. Estimation procedures for the parameters involved in the spectral density function are then investigated. Both the consistency and the asymptotic normality of the estimators of the parameters are established. In addition, a real example is presented to demonstrate the applicability of the estimation procedures.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 99 (2002)
Issue (Month): 2 (June)
Pages: 295-321

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Handle: RePEc:eee:spapps:v:99:y:2002:i:2:p:295-321

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Keywords: Asymptotic theory Fractional Riesz-Bessel motion Nonstationary process Long-range dependence Statistical estimation;

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References

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  1. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  2. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
  3. Peter M. Robinson, 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
  4. Viano, M. C. & Deniau, C. & Oppenheim, G., 1994. "Continuous-time fractional ARMA processes," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 323-336, November.
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Cited by:
  1. Casas, Isabel & Gao, Jiti, 2008. "Econometric estimation in long-range dependent volatility models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 72-83, November.
  2. Casas, Isabel, 2008. "Estimation of stochastic volatility with LRD," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 335-340.
  3. Leonenko, N.N. & Sakhno, L.M., 2006. "On the Whittle estimators for some classes of continuous-parameter random processes and fields," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 781-795, April.
  4. Gao, Jiti, 2002. "Modeling long-range dependent Gaussian processes with application in continuous-time financial models," MPRA Paper 11973, University Library of Munich, Germany, revised 18 Sep 2003.
  5. Anh, V.V. & Leonenko, N.N. & Sakhno, L.M., 2007. "Statistical inference using higher-order information," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 706-742, April.

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