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Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data

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  • Reiß, Markus
  • Todorov, Viktor
  • Tauchen, George

Abstract

We derive a nonparametric test for constant beta over a fixed time interval from high-frequency observations of a bivariate Itô semimartingale. Beta is defined as the ratio of the spot continuous covariation between an asset and a risk factor and the spot continuous variation of the latter. The test is based on the asymptotic behavior of the covariation between the risk factor and an estimate of the residual component of the asset, that is orthogonal (in martingale sense) to the risk factor, over blocks with asymptotically shrinking time span. Rate optimality of the test over smoothness classes is derived.

Suggested Citation

  • Reiß, Markus & Todorov, Viktor & Tauchen, George, 2015. "Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2955-2988.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:2955-2988
    DOI: 10.1016/j.spa.2015.02.008
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    Citations

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    Cited by:

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    2. Li, Jia & Todorov, Viktor & Tauchen, George, 2017. "Adaptive estimation of continuous-time regression models using high-frequency data," Journal of Econometrics, Elsevier, vol. 200(1), pages 36-47.
    3. Li, Jia & Todorov, Viktor & Tauchen, George & Chen, Rui, 2017. "Mixed-scale jump regressions with bootstrap inference," Journal of Econometrics, Elsevier, vol. 201(2), pages 417-432.
    4. Choi, Jungjun & Yang, Xiye, 2022. "Asymptotic properties of correlation-based principal component analysis," Journal of Econometrics, Elsevier, vol. 229(1), pages 1-18.
    5. Chen, Dachuan & Mykland, Per A. & Zhang, Lan, 2024. "Realized regression with asynchronous and noisy high frequency and high dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).
    6. Sun, Yucheng & Xu, Wen & Zhang, Chuanhai, 2023. "Identifying latent factors based on high-frequency data," Journal of Econometrics, Elsevier, vol. 233(1), pages 251-270.
    7. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    8. Aït-Sahalia, Yacine & Kalnina, Ilze & Xiu, Dacheng, 2020. "High-frequency factor models and regressions," Journal of Econometrics, Elsevier, vol. 216(1), pages 86-105.
    9. Andersen, Torben G. & Riva, Raul & Thyrsgaard, Martin & Todorov, Viktor, 2023. "Intraday cross-sectional distributions of systematic risk," Journal of Econometrics, Elsevier, vol. 235(2), pages 1394-1418.
    10. Kong, Xin-Bing & Liu, Cheng, 2018. "Testing against constant factor loading matrix with large panel high-frequency data," Journal of Econometrics, Elsevier, vol. 204(2), pages 301-319.
    11. Kim Christensen & Mikkel Slot Nielsen & Mark Podolskij, 2023. "High-dimensional estimation of quadratic variation based on penalized realized variance," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 331-359, July.

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