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Semiparametric estimation in perturbed long memory series

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  • Josu Arteche

    (University of the Basque Country)

Abstract

The estimation of the memory parameter in perturbed long memory series has recently attracted attention motivated especially by the strong persistence of the volatility in many financial and economic time series and the use of Long Memory in Stochastic Volatility (LMSV) processes to model such a behaviour. This paper discusses frequency domain semiparametric estimation of the memory parameter and proposes an extension of the log periodogram regression which explicitly accounts for the added noise, comparing it, asymptotically and in finite samples, with similar extant techniques. Contrary to the non linear log periodogram regression of Sun and Phillips, we do not use a linear approximation of the logarithmic term which accounts for the added noise. A reduction of the asymptotic bias is achieved in this way and makes possible a faster convergence by permitting a larger bandwidth. Monte Carlo results confirm this bias reduction in finite samples. An application to a series of returns of the Spanish Ibex35 stock index is finally included.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 22.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:22

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Keywords: long memory; stochastic volatility; semiparametric estimation;

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  1. Yixiao Sun & Peter C.B. Phillips, 2002. "Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes," Cowles Foundation Discussion Papers 1366, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
  4. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  5. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
  6. 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.
  7. 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).
  8. 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.
  9. Josu Artech & Peter M Robinson, 1998. "Seasonal and Cyclical Long Memory - (Now published in S Ghosh (ed): Asymptotics, Nonparametrics and Time Series: A Tribute to Madam Lal Puri (Marcel Decker, 1999), pp.115-145.)," STICERD - Econometrics Paper Series /1998/360, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, vol. 114(1), pages 1-27, May.
  11. Perez, Ana & Ruiz, Esther, 2001. "Finite sample properties of a QML estimator of stochastic volatility models with long memory," Economics Letters, Elsevier, vol. 70(2), pages 157-164, February.
  12. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February.
  13. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03.
  14. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  15. 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.
  16. J. Arteche & C. Velasco, 2005. "Trimming and Tapering Semi-Parametric Estimates in Asymmetric Long Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 581-611, 07.
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Citations

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Cited by:
  1. Esther Ruiz & Helena Veiga, 2006. "Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch," Statistics and Econometrics Working Papers ws066016, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Coakley, Jerry & Dollery, Jian & Kellard, Neil, 2008. "The role of long memory in hedging effectiveness," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3075-3082, February.
  3. Josu Arteche, 2012. "Standard and seasonal long memory in volatility: an application to Spanish inflation," Empirical Economics, Springer, vol. 42(3), pages 693-712, June.
  4. Frederiksen, Per & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2012. "Local polynomial Whittle estimation of perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 167(2), pages 426-447.
  5. Bordignon, Silvano & Caporin, Massimiliano & Lisi, Francesco, 2007. "Generalised long-memory GARCH models for intra-daily volatility," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5900-5912, August.
  6. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
  7. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
  8. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus.

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