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Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood

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  • Per Frederiksen
  • Frank S. Nielsen

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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    Abstract

    In this paper, we propose new tests for long memory in stationary and nonstationary time series possibly perturbed by short-run noise which may be serially correlated. The tests are all based on semiparametric estimators and exploit the self-similarity property of long memory processes. We o¤er simulation results that show good size properties of the tests, with power against spurious long memory. An empirical study of daily log-squared returns series of exchange rates and DJIA30 stocks shows that indeed there is long memory in exchange rate volatility and stock return volatility.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/08/rp08_59.pdf
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    Bibliographic Info

    Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-59.

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    Length: 51
    Date of creation: 25 Nov 2008
    Date of revision:
    Handle: RePEc:aah:create:2008-59

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    Web page: http://www.econ.au.dk/afn/

    Related research

    Keywords: Temporal aggregation; semiparametric estimation; fractional integration; self-similarity; perturbed fractional processes.;

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    References

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    1. Arteche González, Jesús María, 2002. "Gaussian Semiparametric Estimation in Long Memory in Stochastic Volatility and Signal Plus Noise Models," BILTOKI 2002-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    2. Nielsen, Morten rregaard, 2004. "Efficient Likelihood Inference In Nonstationary Univariate Models," Econometric Theory, Cambridge University Press, vol. 20(01), pages 116-146, February.
    3. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
    4. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    5. Souza, Leonardo Rocha, 2003. "Temporal Aggregation and Bandwidth Selection in Estimating Long Memory," Economics Working Papers (Ensaios Economicos da EPGE) 478, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    6. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    7. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2009. "Local polynomial Whittle estimation of perturbed fractional processes," Working Papers 1218, Queen's University, Department of Economics.
    9. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
    10. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
    11. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    12. Gil-Alana Luis A, 2003. "Fractional Integration with Bloomfield Disturbances in the Specification of Real Output in the G7 Countries," The B.E. Journal of Macroeconomics, De Gruyter, vol. 3(1), pages 1-15, September.
    13. Souza, Leonardo Rocha, 2003. "The Aliasing Effect, the Fejer Kernel and Temporally Aggregated Long Memory Processes," Economics Working Papers (Ensaios Economicos da EPGE) 470, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    14. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    15. Arteche González, Jesús María, 2005. "Semiparametric estimation in perturbed long memory series," BILTOKI 2005-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    16. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    17. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    18. Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 445-470.
    19. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
    20. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics.
    21. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
    22. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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    24. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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    Cited by:
    1. Norman R. Swanson & Valentina Corradi, 2011. "Predictive Density Construction and Accuracy Testing with Multiple Possibly Misspecified Diffusion Models," Departmental Working Papers 201112, Rutgers University, Department of Economics.
    2. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1433-1445, October.

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