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Testing against constant factor loading matrix with large panel high-frequency data

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  • Kong, Xin-Bing
  • Liu, Cheng

Abstract

In this paper, we introduce a nonparametric test against the constancy of the factor loading matrix of a high-dimensional continuous-time factor model using high-frequency data. The central limit theorems on the test statistics with and without perturbation are established under the null hypothesis that the factor loading matrix is constant as time evolves. The tests perform well in size and power. Interestingly, the test statistic without perturbation converges at a rate that depends not only on the sample size but also on the dimension through the cross-sectional dependence of the residual process, which is a distinctive feature that contrasts with the low-dimensional setting. Extensive numerical studies, including Monte Carlo simulations and real data analysis, validate the performance of our test.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:204:y:2018:i:2:p:301-319
    DOI: 10.1016/j.jeconom.2018.03.001
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    1. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    2. Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 412-428, March.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    5. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    6. 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.
    7. Viktor Todorov & George Tauchen, 2012. "The Realized Laplace Transform of Volatility," Econometrica, Econometric Society, vol. 80(3), pages 1105-1127, May.
    8. Shephard, Neil & Xiu, Dacheng, 2017. "Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading," Journal of Econometrics, Elsevier, vol. 201(1), pages 19-42.
    9. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    10. Xin-Bing Kong, 2017. "On the number of common factors with high-frequency data," Biometrika, Biometrika Trust, vol. 104(2), pages 397-410.
    11. Jianqing Fan & Alex Furger & Dacheng Xiu, 2016. "Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 489-503, October.
    12. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
    13. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    14. 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.
    15. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
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    More about this item

    Keywords

    Continuous-time factor model; Factor loading matrix; High dimensional itô process;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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