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On the Whittle estimators for some classes of continuous-parameter random processes and fields

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  • Leonenko, N.N.
  • Sakhno, L.M.

Abstract

Continuous version of the Whittle contrast functional supplied with a specific weight function is proposed for the estimation of continuous-parameter stochastic processes and fields observed continuously. The results on consistency and asymptotic normality of the estimators are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:781-795
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    References listed on IDEAS

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    1. Jiti Gao & Vo Anh & Chris Heyde & Quang Tieng, 2001. "Parameter Estimation of Stochastic Processes with Long‐range Dependence and Intermittency," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 517-535, September.
    2. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    3. Gao, Jiti & Anh, Vo & Heyde, Chris, 2002. "Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 295-321, June.
    4. Heyde, C. C. & Gay, R., 1989. "On asymptotic quasi-likelihood estimation," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 223-236, April.
    5. 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.
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    Cited by:

    1. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    2. 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.
    3. Hira Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    4. A. V. Ivanov & N. N. Leonenko & I. V. Orlovskyi, 2020. "On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 129-169, April.
    5. Li, Ming & Zhang, Peidong & Leng, Jianxing, 2016. "Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 189-199.
    6. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    7. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.

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