An adaptive jump test for discretely observed high-frequency semimartingales is constructed by merging the Aït-Sahalia-Jacod ratio statistic and Lee-Mykland extreme-return statistic with the Cauchy combination rule, yielding asymptotic independence and closed-form power under the continuous null.
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A new U-statistic white noise test for high-dimensional series achieves asymptotic normality under the null via martingale differences and spectral conditions on the covariance matrix, without cross-sectional independence.
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Adaptive Test for Jump
An adaptive jump test for discretely observed high-frequency semimartingales is constructed by merging the Aït-Sahalia-Jacod ratio statistic and Lee-Mykland extreme-return statistic with the Cauchy combination rule, yielding asymptotic independence and closed-form power under the continuous null.
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Tests for white noise via asymptotically independent U-statistics in high-dimensions
A new U-statistic white noise test for high-dimensional series achieves asymptotic normality under the null via martingale differences and spectral conditions on the covariance matrix, without cross-sectional independence.