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Maximum likelihood estimation of linear continuous time long memory processes with discrete time data

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  • Henghsiu Tsai
  • K. S. Chan

Abstract

Summary. We develop a new class of time continuous autoregressive fractionally integrated moving average (CARFIMA) models which are useful for modelling regularly spaced and irregu‐larly spaced discrete time long memory data. We derive the autocovariance function of a stationary CARFIMA model and study maximum likelihood estimation of a regression model with CARFIMA errors, based on discrete time data and via the innovations algorithm. It is shown that the maximum likelihood estimator is asymptotically normal, and its finite sample properties are studied through simulation. The efficacy of the approach proposed is demonstrated with a data set from an environmental study.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:5:p:703-716
    DOI: 10.1111/j.1467-9868.2005.00522.x
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    Cited by:

    1. Vicky Fasen-Hartmann & Celeste Mayer, 2022. "Whittle estimation for continuous-time stationary state space models with finite second moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 233-270, April.
    2. 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.
    3. Cheng, Tsung-Lin, 2009. "An efficient algorithm for estimating a change-point," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 559-565, March.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.

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