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Inference of Seasonal Long-memory Time Series with Measurement Error


  • Henghsiu Tsai
  • Heiko Rachinger
  • Edward M.H. Lin


type="main" xml:id="sjos12099-abs-0001"> We consider the Whittle likelihood estimation of seasonal autoregressive fractionally integrated moving-average models in the presence of an additional measurement error and show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement errors, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non-standard asymptotic null distribution of this LR test and the limiting distribution of LR test under a sequence of local alternatives. Because in practice, we do not know the order of the seasonal autoregressive fractionally integrated moving-average model, we consider three modifications of the LR test that takes model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by a real-life example.

Suggested Citation

  • Henghsiu Tsai & Heiko Rachinger & Edward M.H. Lin, 2015. "Inference of Seasonal Long-memory Time Series with Measurement Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 137-154, March.
  • Handle: RePEc:bla:scjsta:v:42:y:2015:i:1:p:137-154

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    References listed on IDEAS

    1. Hosoya, Yuzo, 1996. "The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence," Journal of Econometrics, Elsevier, vol. 73(1), pages 217-236, July.
    2. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    3. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    4. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
    5. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    6. Palma, Wilfredo & Bondon, Pascal, 2003. "On the eigenstructure of generalized fractional processes," Statistics & Probability Letters, Elsevier, vol. 65(2), pages 93-101, November.
    7. Gil-Alana, Luis A., 2002. "Seasonal long memory in the aggregate output," Economics Letters, Elsevier, vol. 74(3), pages 333-337, February.
    8. 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.
    9. Ray, Bonnie K., 1993. "Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model," International Journal of Forecasting, Elsevier, vol. 9(2), pages 255-269, August.
    10. Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July.
    11. Tanaka, Katsuto, 2002. "A Unified Approach To The Measurement Error Problem In Time Series Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 278-296, April.
    12. Wilfredo Palma & Ngai Hang Chan, 2005. "Efficient Estimation of Seasonal Long-Range-Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 863-892, November.
    13. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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    Cited by:

    1. Asai, M. & McAleer, M.J. & Peiris, S., 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Econometric Institute Research Papers EI2017-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    3. Asai, M. & Peiris, S. & McAleer, M.J. & Allen, D.E., 2018. "Cointegrated Dynamics for A Generalized Long Memory Process," Econometric Institute Research Papers EI 2018-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Manabu Asai & Shelton Peiris & Michael McAleer & David E. Allen, 2018. "Cointegrated Dynamics for A Generalized Long Memory Process: An Application to Interest Rates," Documentos de Trabajo del ICAE 2018-22, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    5. Reisen, Valdério Anselmo & Monte, Edson Zambon & da Conceição Franco, Glaura & Sgrancio, Adriano Marcio & Molinares, Fábio Alexander Fajardo & Bondon, Pascal & Ziegelmann, Flávio Augusto & Abraham, Bo, 2018. "Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 27-43.

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