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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. 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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    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Arteche, J. & Orbe, J., 2005. "Bootstrapping the log-periodogram regression," Economics Letters, Elsevier, vol. 86(1), pages 79-85, January.
    10. 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(4), pages 686-710, August.
    11. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive semiparametric estimation of the memory parameter," LSE Research Online Documents on Economics 2082, London School of Economics and Political Science, LSE Library.
    12. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
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    1. 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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