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Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes

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Author Info
Yixiao Sun (Dept. Economics, Yale University)
Peter C.B. Phillips () (Cowles Foundation)

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Abstract

This paper studies fractional processes that may be perturbed by weakly dependent time series. The model for a perturbed fractional process has a components framework in which there may be components of both long and short memory. All commonly used estimates of the long memory parameter (such as log periodogram (LP) regression) may be used in a components model where the data are affected by weakly dependent perturbations, but these estimates can suffer from serious downward bias. To circumvent this problem, the present paper proposes a new procedure that allows for the possible presence of additive perturbations in the data. The new estimator resembles the LP regression estimator but involves an additional (nonlinear) term in the regression that takes account of possible perturbation effects in the data. Under some smoothness assumptions at the origin, the bias of the new estimator is shown to disappear at a faster rate than that of the LP estimator, while its asymptotic variance is inflated only by a multiplicative constant. In consequence, the optimal rate of convergence to zero of the asymptotic MSE of the new estimator is faster than that of the LP estimator. Some simulation results demonstrate the viability and the bias-reducing feature of the new estimator relative to the LP estimator in finite samples. A test for the presence of perturbations in the data is given.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1366.

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Length: 40 pages
Date of creation: May 2002
Date of revision:
Publication status: Published in Journal of Econometrics (2003), 115(2): 355-389
Handle: RePEc:cwl:cwldpp:1366

Note: CFP 1077.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Asymptotic bias; Asymptotic normality; Bias reduction; Fractional components model; Perturbed fractional process; Rate of convergence; Testing perturbations;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

References listed on IDEAS
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  1. Donald W.K. Andrews & Yixiao Sun, 2001. "Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1293, Cowles Foundation, Yale University. [Downloadable!]
  2. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July. [Downloadable!] (restricted)
    Other versions:
  3. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March. [Downloadable!] (restricted)
    Other versions:
  4. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics. [Downloadable!]
    Other versions:
  5. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November. [Downloadable!] (restricted)
  6. Clive W.J. Granger & Francesc Marmol, 1997. "The Correlogram of a Long Memory Process Plus a Simple Noise," University of California at San Diego, Economics Working Paper Series 97-29, Department of Economics, UC San Diego. [Downloadable!]
  7. 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. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
  9. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
  10. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Casas, Isabel & Gao, Jiti, 2006. "Econometric estimation in long-range dependent volatility models: Theory and practice," MPRA Paper 11981, University Library of Munich, Germany, revised Aug 2007. [Downloadable!]
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  2. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series /2006/497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  3. Nuno Cassola & Claudio Morana, 2007. "Comovements in Volatility in the Euro Money Market," ICER Working Papers 7-2007, ICER - International Centre for Economic Research. [Downloadable!]
  4. Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2008. "Local polynomial Whittle estimation of perturbed fractional processes," CREATES Research Papers 2008-29, School of Economics and Management, University of Aarhus. [Downloadable!]
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  5. Josu Arteche, 2005. "Semiparametric estimation in perturbed long memory series," BILTOKI 200502, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística). [Downloadable!]
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  6. Claudio Morana, 2007. "On the macroeconomic causes of exchange rates volatility," ICER Working Papers 8-2007, ICER - International Centre for Economic Research. [Downloadable!]
  7. Claudio Morana, 2006. "Multivariate modelling of long memory processes with common components," ICER Working Papers 40-2006, ICER - International Centre for Economic Research. [Downloadable!]
  8. Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Bias-reduced estimation of long memory stochastic volatility," CREATES Research Papers 2008-35, School of Economics and Management, University of Aarhus. [Downloadable!]
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  9. Claudio Morana, 2004. "The Japanese Deflation: Has It Had Real Effects? Could It Have Been Avoided?," ICER Working Papers 29-2004, ICER - International Centre for Economic Research. [Downloadable!]
  10. Haldrup, Niels & Nielsen, Morten Oe., . "Estimation of Fractional Integration in the Presence of Data Noise," Economics Working Papers 2003-10, School of Economics and Management, University of Aarhus. [Downloadable!]
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  11. Andrea Beltratti & Claudio Morana, 2005. "Structural Breaks and Common Factors in the Volatility of the Fama-French Factor Portfolios," ICER Working Papers 23-2005, ICER - International Centre for Economic Research. [Downloadable!]
  12. Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Quantitative Finance Papers 0706.1836, arXiv.org. [Downloadable!]
  13. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA. [Downloadable!]
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  14. Andrea Beltratti & Claudio Morana, 2004. "Breaks and Persistency: Macroeconomic Causes of Stock Market Volatility," Working Papers 20, SEMEQ Department - Faculty of Economics - University of Eastern Piedmont. [Downloadable!]
  15. Claudio Morana, 2007. "Estimating, Filtering and Forecasting Realized Betas," ICER Working Papers - Applied Mathematics Series 6-2007, ICER - International Centre for Economic Research. [Downloadable!]
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