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Ratio tests under limiting normality

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  • Uwe Hassler
  • Mehdi Hosseinkouchack

Abstract

We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. The Karhunen–Loève theorem is employed to compute weighted averages. The test statistics are ratios of quadratic forms of these averages and hence scale-invariant, also called self-normalizing: The scaling parameter cancels asymptotically. Limiting distributions are obtained. Critical values and asymptotic local power functions can be calculated by standard numerical means. The ratio tests are directed against local alternatives and turn out to be almost as powerful as optimal competitors, without being plagued by nuisance parameters at the same time. Also in finite samples they perform well relative to self-normalizing competitors.

Suggested Citation

  • Uwe Hassler & Mehdi Hosseinkouchack, 2019. "Ratio tests under limiting normality," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 793-813, August.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:7:p:793-813
    DOI: 10.1080/07474938.2018.1427296
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    Cited by:

    1. Richard K. Crump & Nikolay Gospodinov, 2022. "On the Factor Structure of Bond Returns," Econometrica, Econometric Society, vol. 90(1), pages 295-314, January.
    2. Ben Ammar, Imen & Hellara, Slaheddine, 2021. "Intraday interactions between high-frequency trading and price efficiency," Finance Research Letters, Elsevier, vol. 41(C).

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