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High dimensional regression coefficient test with high frequency data
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DOI：10.1016/j.jeconom.2024.105812.png)
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Abstract
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This paper presents the first study on high-dimensional regression coefficient tests with high-frequency financial data. These tests allow the number of regressors to be larger than the number of observations within each estimation block and can grow to infinity in asymptotics. In this paper, the sum-type test and max-type test have been proposed, where the former is suitable for the dense alternative (many small betas) and the latter is suitable for the sparse alternative (a very small number of large betas). By showing the asymptotic independence between the sum-type test and max-type test, the paper proposes a third test – Fisher’s combination test, which is robust to both dense and sparse alternatives. The paper derives the limiting null distributions of the three proposed tests and analyzes the asymptotic behavior of their powers. Monte Carlo simulations demonstrate the validity of the theoretical results developed in this paper. Empirical study shows the impact of high frequency (HF) factors when being added to a Fama–French-style factor model. We found that the HF effects are time varying. The proposed tests can help identify those time periods when the HF factors carry (significant) incremental information for the test asset. Our tests could shed light on market timing in a trading strategy.
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