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Bootstrap‐based bandwidth choice for log‐periodogram regression

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  • Josu Arteche
  • Jesus Orbe

Abstract

. The choice of the bandwidth in the local log‐periodogram regression is of crucial importance for estimation of the memory parameter of a long memory time series. Different choices may give rise to completely different estimates, which may lead to contradictory conclusions, for example about the stationarity of the series. We propose here a data‐driven bandwidth selection strategy that is based on minimizing a bootstrap approximation of the mean‐squared error (MSE). Its behaviour is compared with other existing techniques for optimal bandwidth selection in a MSE sense, revealing its better performance in a wider class of models. The empirical applicability of the proposed strategy is shown with two examples: the widely analysed in a long memory context Nile river annual minimum levels and the input gas rate series of Box and Jenkins.

Suggested Citation

  • Josu Arteche & Jesus Orbe, 2009. "Bootstrap‐based bandwidth choice for log‐periodogram regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 591-617, November.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:6:p:591-617
    DOI: 10.1111/j.1467-9892.2009.00629.x
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    References listed on IDEAS

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    1. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
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    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.
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    6. 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.
    7. Josu Arteche & Peter M. Robinson, 2000. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 1-25, January.
    8. 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, March.
    9. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    10. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    11. Silva, E.M. & Franco, G.C. & Reisen, V.A. & Cruz, F.R.B., 2006. "Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1002-1011, November.
    12. 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.
    13. Giraitis, L. & Robinson, P.M., 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," LSE Research Online Documents on Economics 291, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. J. Arteche, 2012. "Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 440-474.
    2. Arteche, Josu & Orbe, Jesus, 2017. "A strategy for optimal bandwidth selection in Local Whittle estimation," Econometrics and Statistics, Elsevier, vol. 4(C), pages 3-17.

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