A note on mixingale limit theorems and stable convergence in law

Shin S. Ikeda

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 19, 9377-9387

Abstract: A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.

Date: 2017
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DOI: 10.1080/03610926.2016.1208238

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