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An Efficient Taper for Potentially Overdifferenced Long‐memory Time Series

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  • Clifford M. Hurvich
  • Willa W. Chen

Abstract

We propose a new complex‐valued taper and derive the properties of a tapered Gaussian semiparametric estimator of the long‐memory parameter dε (−0.5, 1.5). The estimator and its accompanying theory can be applied to generalized unit root testing. In the proposed method, the data are differenced once before the taper is applied. This guarantees that the tapered estimator is invariant with respect to deterministic linear trends in the original series. Any detrimental leakage effects due to the potential noninvertibility of the differenced series are strongly mitigated by the taper. The proposed estimator is shown to be more efficient than existing invariant tapered estimators. Invariance to kth order polynomial trends can be attained by differencing the data k times and then applying a stronger taper, which is given by the kth power of the proposed taper. We show that this new family of tapers enjoys strong efficiency gains over comparable existing tapers. Analysis of both simulated and actual data highlights potential advantages of the tapered estimator of d compared with the nontapered estimator.

Suggested Citation

  • Clifford M. Hurvich & Willa W. Chen, 2000. "An Efficient Taper for Potentially Overdifferenced Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 155-180, March.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:2:p:155-180
    DOI: 10.1111/1467-9892.00179
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    Cited by:

    1. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    2. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, University Library of Munich, Germany.
    3. Shuping Shi & Jun Yu, 2023. "Volatility Puzzle: Long Memory or Antipersistency," Management Science, INFORMS, vol. 69(7), pages 3861-3883, July.
    4. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    5. Gannaz, Irène, 2023. "Asymptotic normality of wavelet covariances and multivariate wavelet Whittle estimators," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 485-534.
    6. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    7. Guillermo Ferreira & Jorge Mateu & Jose A. Vilar & Joel Muñoz, 2021. "Bootstrapping regression models with locally stationary disturbances," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 341-363, June.
    8. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    9. Saeed Heravi & Kerry Patterson, 2005. "Optimal And Adaptive Semi‐Parametric Narrowband And Broadband And Maximum Likelihood Estimation Of The Long‐Memory Parameter For Real Exchange Rates," Manchester School, University of Manchester, vol. 73(2), pages 165-213, March.
    10. Arteche González, Jesús María, 2020. "Frequency Domain Local Bootstrap in long memory time series," BILTOKI info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    11. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.

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