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A bootstrap approximation for the distribution of the Local Whittle estimator

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  • Arteche, Josu
  • Orbe, Jesus

Abstract

The asymptotic properties of the Local Whittle estimator of the memory parameter d have been widely analysed and its consistency and asymptotic distribution have been obtained for values of d∈(−1/2,1] in a wide range of situations. However, the asymptotic distribution may be a poor approximation of the exact one in several cases, e.g. with small sample sizes or even with larger samples when d>0.75. In other situations the asymptotic distribution is unknown, as for example in a noninvertible context or in some nonlinear transformations of long memory processes, where only consistency is obtained. For all these cases a bootstrap strategy based on resampling a (perhaps locally) standardised periodogram is proposed. A Monte Carlo analysis shows that this strategy leads to a good approximation of the exact distribution of the Local Whittle estimator in those situations where the asymptotic distribution is not reliable.

Suggested Citation

  • Arteche, Josu & Orbe, Jesus, 2016. "A bootstrap approximation for the distribution of the Local Whittle estimator," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 645-660.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:645-660
    DOI: 10.1016/j.csda.2015.03.014
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    Cited by:

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    2. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2017. "The Memory of Volatility," Hannover Economic Papers (HEP) dp-601, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
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    5. Ying Lun Cheung & Uwe Hassler, 2020. "Whittle-type estimation under long memory and nonstationarity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 363-383, September.

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