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Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes

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  • Henghsiu Tsai
  • K. S. Chan

Abstract

Tsai and Chan (2003) has recently introduced the Continuous‐time Auto‐Regressive Fractionally Integrated Moving‐Average (CARFIMA) models useful for studying long‐memory data. We consider the estimation of the CARFIMA models with discrete‐time data by maximizing the Whittle likelihood. We show that the quasi‐maximum likelihood estimator is asymptotically normal and efficient. Finite‐sample properties of the quasi‐maximum likelihood estimator and those of the exact maximum likelihood estimator are compared by simulations. Simulations suggest that for finite samples, the quasi‐maximum likelihood estimator of the Hurst parameter is less biased but more variable than the exact maximum likelihood estimator. We illustrate the method with a real application.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:5:p:691-713
    DOI: 10.1111/j.1467-9892.2005.00422.x
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. Anne Philippe & Caroline Robet & Marie-Claude Viano, 2021. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 375-400, April.
    6. Kuswanto, Heri, 2009. "A New Simple Test Against Spurious Long Memory Using Temporal Aggregation," Hannover Economic Papers (HEP) dp-425, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Chen, Chun-Da & Chiang, Shu-Mei & Huang, Tze-Chin, 2020. "The contagion effects of volatility indices across the U.S. and Europe," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    8. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 583-597, December.
    9. Chiang, Shu-Mei & Chen, Chun-Da & Huang, Chien-Ming, 2019. "Analyzing the impacts of foreign exchange and oil price on biofuel commodity futures," Journal of International Money and Finance, Elsevier, vol. 96(C), pages 37-48.
    10. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    11. Sun, Qi & Xu, Weijun & Xiao, Weilin, 2013. "An empirical estimation for mean-reverting coal prices with long memory," Economic Modelling, Elsevier, vol. 33(C), pages 174-181.
    12. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.

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