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February 2018 How the Instability of Ranks Under Long Memory Affects Large-Sample Inference
Shuyang Bai, Murad S. Taqqu
Statist. Sci. 33(1): 96-116 (February 2018). DOI: 10.1214/17-STS633


Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called “Hermite rank.” There is a different limit for each Hermite rank. From a statistical point of view, however, we argue that a rank other than one is unstable, whereas, a rank equal to one is stable. We provide empirical evidence supporting this argument. This has important consequences. Assuming a higher-order rank when it is not really there usually results in underestimating the order of the fluctuations of the statistic of interest. We illustrate this through various examples involving the sample variance, the empirical processes and the Whittle estimator.


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Shuyang Bai. Murad S. Taqqu. "How the Instability of Ranks Under Long Memory Affects Large-Sample Inference." Statist. Sci. 33 (1) 96 - 116, February 2018.


Published: February 2018
First available in Project Euclid: 2 February 2018

zbMATH: 07031393
MathSciNet: MR3757507
Digital Object Identifier: 10.1214/17-STS633

Keywords: Hermite rank , instability , large-sample inference , long memory , long-range dependence , non-Gaussian limit , power rank

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.33 • No. 1 • February 2018
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