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  Current Development in Theory and Applications of Wavelets  
 ISSN: 0973-5607
 
 
 

     Current Development in Theory and Applications of Wavelets
    Volume 3, Issue 2, Pages 121 - 130 (August 2009)


WAVELETS FOR ESTIMATING THE FRACTIONAL PARAMETER IN NON-STATIONARY ARFIMA PROCESSES

S. R. C. Lopes (Brazil) and A. Pinheiro (Brazil)

Received July 9, 2009

References:



[1] J. Beran, Statistics for Long-memory Processes, Chapman and Hall, New York, 1994.

[2] J. Geweke and S. Porter-Hudak, The estimation and application of long memory time series models, J. Time Ser. Anal. 4(4) (1983), 221-238.

[3] J. R. M. Hosking, Fractional differencing, Biometrika 68(1) (1981), 165-167.

[4] H. E. Hurst, Long-term storage capacity of reservoirs, Trans. Amer. Soc. Civil Eng. 116 (1951), 770-799.

[5] M. J. Jensen, Using wavelets to obtain a consistent ordinary least squares estimator of the long memory parameter, J. Forecast. 18(1) (1999), 17-32.

[6] S. R. C. Lopes, Long-range dependence in mean and volatility: models, estimation and forecasting, In and Out of Equilibrium 2, V. Sidoravicius and M. E. Vares, eds., Birkhäuser, Basel, Vol. 60, 2008, pp. 497-525.

[7] T. C. Mills, The Econometric Modelling of Financial Time Series, Cambridge University Press, Cambridge, UK, 1997.

[8] D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, Cambridge, UK, 2000.

[9] V. A. Reisen, Estimation of the fractional difference parameter in the model using the smoothed periodogram, J. Time Ser. Anal. 15(3) (1994), 335-350.

[10] B. Vidakovic, Statistical Modeling by Wavelets, John Wiley and Sons, Inc., New York, 1999.

[11] P. Wu and N. Crato, New tests for stationarity and parity reversion: evidence on New Zealand real exchange rates, Empirical Economics 20(4) (1995), 599-613.

Keywords and phrases: Haar system, time series, CWT, long range dependence.

 


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