Inference for Nonparametric High-Frequency Estimators with an Application to Time Variation in Betas

References

• Adrian, T., and Franzoni, F. (2009), “Learning about beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM,” Journal of Empirical Finance, 16, 537–556. DOI: 10.1016/j.jempfin.2009.02.003.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., Fan, J., and Xiu, D. (2010), “High-Frequency Covariance Estimates with Noisy and Asynchronous Data,” Journal of the American Statistical Association, 105, 1504–1517. DOI: 10.1198/jasa.2010.tm10163.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Jacod, J. (2014), High-Frequency Financial Econometrics, Princeton, NJ: Princeton University Press.
   Google Scholar
• Aït-Sahalia, Y., Kalnina, I., and Xiu, D. (2020), “High-Frequency Factors Models and Regressions,” Journal of Econometrics, 216, 86–105. DOI: 10.1016/j.jeconom.2020.01.007.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Mancini, L. (2008), “Our of Sample Forecasts of Quadratic Variation,” Journal of Econometrics, 147, 17–33. DOI: 10.1016/j.jeconom.2008.09.015.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., Mykland, P. A., and Zhang, L. (2011), “Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise,” Journal of Econometrics, 160, 190–203. DOI: 10.1016/j.jeconom.2010.03.028.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Xiu, D. (2019), “Principal Component Analysis of High Frequency Data,” Journal of the American Statistical Association, 114, 287–303. DOI: 10.1080/01621459.2017.1401542.
   Web of Science ®Google Scholar
• Andersen, T., T. Bollerslev, and N. Meddahi (2005a), “Correcting the Errors: Volatility Forecast Evaluation Using High Frequency Data and Realized Volatilities,” Econometrica, 73, 279–296. DOI: 10.1111/j.1468-0262.2005.00572.x.
   Web of Science ®Google Scholar
• Andersen, T., T. Bollerslev, and N. Meddahi (2005b), “A Framework for Exploring the Macroeconomic Determinants of Systematic Risk,” American Economic Review, 95, 398–404.
   Web of Science ®Google Scholar
• ——— (2006), “Realized Beta: Persistence and Predictability,” in Advances in Econometrics: Econometric Analysis of Economic and Financial Time Series in Honor of R.F. Engle and C.W.J. Granger, eds. T. Fomby and D. Terrell (pp. 1–39). Bingley: Emerald Publishing.
   Google Scholar
• Andrews, D. (1991), “Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation,” Econometrica, 59, 817–858. DOI: 10.2307/2938229.
   Web of Science ®Google Scholar
• Bandi, F. M., and Russell, J. R. (2005), “Realized Covariation, Realized Beta, and Microstructure Noise,” Technical Reports, University of Chicago.
   Google Scholar
• Bandi, F. M., and Russell, J. R (2006), “Separating Microstructure Noise from Volatility,” Journal of Financial Economics, 79, 655–692.
   Web of Science ®Google Scholar
• Bandi, F. M., and Russell, J. R (2008), “Microstructure Noise, Realized Volatility and Optimal Sampling,” Review of Economic Studies, 75, 339–369.
   Web of Science ®Google Scholar
• Bandi, F. M., and Russell, J. R (2011), “Market Microstructure Noise, Integrated Variance Estimators, and the Accuracy of Asymptotic Approximations,” Journal of Econometrics, 160, 145–159.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., and Shephard, N. (2008), “Designing Realized Kernels to Measure Ex-post Variation of Equity Prices in the Presence of Noise,” Econometrica, 76, 1481–1536.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., and Shephard, N (2009), “Realised Kernels in Practice: Trades and Quotes,” Econometrics Journal, 12, C1–C32.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., and Shephard, N (2011), “Multivariate Realised Kernels: Consistent Positive Semi-definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading,” Journal of Econometrics, 162, 149–169.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O. E., and Shephard, N. (2004), “Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics,” Econometrica, 72, 885–925. DOI: 10.1111/j.1468-0262.2004.00515.x.
   Web of Science ®Google Scholar
• Bekaert, G., and Wu, G. (2000), “Asymmetric Volatility and Risk in Equity Markets,” Review of Financial Studies, 13, 1–42. DOI: 10.1093/rfs/13.1.1.
   Web of Science ®Google Scholar
• Bibinger, M. (2012), “An Estimator for the Quadratic Covariation of Asynchronously Observed Ito Processes with Noise: Asymptotic Distribution Theory,” Stochastic Processes and their Applications, 122, 2411–2453. DOI: 10.1016/j.spa.2012.04.002.
   Web of Science ®Google Scholar
• Bibinger, M., and Reiss, M. (2014), “Spectral Estimation of Covolatility from Noisy Observations Using Local Weights,” Scandinavian Journal of Statistics, 41, 23–50. DOI: 10.1111/sjos.12019.
   Web of Science ®Google Scholar
• Bollerslev, T., and Zhang, B. Y. B. (2003), “Measuring and Modelling Systematic Risk in Factor Pricing Models Using High-Frequency Data,” Journal of Empirical Finance, 10, 533–558. DOI: 10.1016/S0927-5398(03)00004-5.
   Google Scholar
• Braun, P. A., Nelson, D. B., and Sunier, A. M. (1995), “Good News, Bad News, Volatility, and Betas,” Journal of Finance, 50, 1575–1603. DOI: 10.1111/j.1540-6261.1995.tb05189.x.
   Web of Science ®Google Scholar
• Christensen, K., Kinnebrock, S., and Podolskij, M. (2010), “Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data,” Journal of Econometrics, 159, 116–133. DOI: 10.1016/j.jeconom.2010.05.001.
   Web of Science ®Google Scholar
• Christensen, K., Podolskij, M., Thamrongrat, N., and Veliyev, B. (2017), “Inference from High-Frequency Data: A Subsampling Approach,” Journal of Econometrics, 197, 245–272. DOI: 10.1016/j.jeconom.2016.07.010.
   Web of Science ®Google Scholar
• Fama, E. F., and French, K. R. (1992), “The Cross-Section of Expected Stock Returns,” The Journal of Finance, 47, 427–465. DOI: 10.1111/j.1540-6261.1992.tb04398.x.
   Web of Science ®Google Scholar
• Fama, E. F., and MacBeth, J. D. (1973), “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, 81, 607–636. DOI: 10.1086/260061.
   Web of Science ®Google Scholar
• Griffin, J. E., and Oomen, R. C. (2008), “Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?” Econometric Reviews, 27, 230–253. DOI: 10.1080/07474930701873341.
   Web of Science ®Google Scholar
• Hansen, P. R., and Lunde, A. (2006), “Realized Variance and Market Microstructure Noise,” Journal of Business and Economic Statistics, 24, 127–161. DOI: 10.1198/073500106000000071.
   Web of Science ®Google Scholar
• Hansen, P. R., and Lunde, A (2014), “Estimating the Persistence and the Autocorrelation Function of a Time Series that is Measured with Error,” Econometric Theory, 30, 60–93.
   Web of Science ®Google Scholar
• Hayashi, T., Jacod, J., and Yoshida, N. (2011), “Irregular Sampling and Central Limmit Theorems for Power Variations: The Continuous Case,” Annales de l’Institut Henri Poincaré, 47, 1197–1218.
   Google Scholar
• Heston, S. (1993), “A Closed-form Solution for Options with Stochastic Volatility with Applications to Bonds and Currency Options,” Review of Financial Studies, 6, 327–343. DOI: 10.1093/rfs/6.2.327.
   Web of Science ®Google Scholar
• Ikeda, S. S. (2016), “A Bias-Corrected Estimator of the Covariation Matrix of Multiple Security Prices when both Microstructure Effects and Sampling Durations are Persistent and Endogenous,” Journal of Econometrics, 193, 203–214. DOI: 10.1016/j.jeconom.2016.02.016.
   Web of Science ®Google Scholar
• Jacod, J., and Rosenbaum, M. (2015), “Estimation of Volatility Functionals: The Case of a n Window,” in Large Deviations and Asymptotic Methods in Finance, eds. P. K. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, and J. Teichmann (pp. 559–590), Cham: Springer.
   Google Scholar
• Jostova, G., and Philipov, A. (2005), “Bayesian Analysis of Stochastic Betas,” Journal of Financial and Quantitative Analysis, 40, 747–778. DOI: 10.1017/S0022109000001964.
   Web of Science ®Google Scholar
• Kalnina, I. (2011), “Subsampling High Frequency Data,” Journal of Econometrics, 161, 262–283. DOI: 10.1016/j.jeconom.2010.12.011.
   Web of Science ®Google Scholar
• Kalnina, I., and Linton, O. (2007), “Inference about Realized Volatiolity Using Infill Subsampling,” Technical Report, London School of Economics.
   Google Scholar
• Kalnina, I., and Tewou, K. (2019), “Cross-Sectional Dependence in Idiosyncratic Volatility,” Technical Report, North Carolina State University.
   Google Scholar
• Lahiri, S. N., Kaiser, M. S., Cressie, N., and Hsu, N.-J. (1999), “Prediction of Spatial Cumulative Distribution Functions Using Subsampling,” Journal of the American Statistical Association, 94, 86–97. DOI: 10.1080/01621459.1999.10473821.
   Web of Science ®Google Scholar
• Lazarus, E., Lewis, D. J., Stock, J. H., and Watson, M. W. (2018), “HAR Inference: Recommendations for Practice,” Journal of Business and Economic Statistics, 36, 541–559. DOI: 10.1080/07350015.2018.1506926.
   Web of Science ®Google Scholar
• Li, J., Todorov, V., and Tauchen, G. (2017), “Adaptive Estimation of Continuous-Time Regression Models using High-Frequency Data,” Journal of Econometrics, 200, 36–47. DOI: 10.1016/j.jeconom.2017.01.010.
   Web of Science ®Google Scholar
• Mancini, C. (2001), “Disentangling the Jumps of the Diffusion in a Geometric Jumping Brownian Motion,” Giornale dell’Istituto Italiano degli Attuari, 64, 19–47.
   Google Scholar
• Mykland, P. A., and Zhang, L. (2006), “ANOVA for Diffusions and Itô Processes,” Annals of Statistics, 34, 1931–1963.
   Web of Science ®Google Scholar
• Mykland, P. A., and Zhang, L (2017), “Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance,” Econometrica, 85, 197–31.
   Web of Science ®Google Scholar
• Newey, W. K., and West, K. D. (1987), “A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, 55, 703–708. DOI: 10.2307/1913610.
   Web of Science ®Google Scholar
• Patton, A., and Verardo, M. (2012), “Does Beta Move with News? Firm-Specific Information Flows and Learning about Profitability,” Review of Financial Studies, 25, 2789–2839. DOI: 10.1093/rfs/hhs073.
   Web of Science ®Google Scholar
• Politis, D. N., and Romano, J. P. (1994), “Large Sample Confidence Regions Based on Subsamples Under Minimal Assumptions,” Annals of Statistics, 22, 2031–2050.
   Web of Science ®Google Scholar
• Politis, D. N., Romano, J. P., and Wolf, M. (1999), Subsampling, New York: Springer-Verlag.
   Google Scholar
• Todorov, V., and Bollerslev, T. (2010), “Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks,” Journal of Econometrics, 157, 220–235. DOI: 10.1016/j.jeconom.2009.11.010.
   Web of Science ®Google Scholar
• Varneskov, R. T. (2016), “Flat-Top Realized Kernel Estimation of Quadratic Covariation with Nonsynchronous and NOisy Asset Prices,” Journal of Business and Economic Statistics, 34, 1–22. DOI: 10.1080/07350015.2015.1005622.
   Web of Science ®Google Scholar
• Vetter, M. (2012), “Estimation of Integrated Volatility of Volatility with Applications to Goodness-of-fit Testing,” Technical Report, Ruhr-Universität Bochum.
   Google Scholar
• Yang, X. (2020), “Time-Invariant Restrictions of Volatility Functionals: Efficient Estimation and Specification Tests,” Journal of Econometrics, 215, 486–516. DOI: 10.1016/j.jeconom.2019.10.003.
   Web of Science ®Google Scholar
• Zhang, L. (2011), “Estimating Covariation: Epps Effect and Microstructure Noise,” Journal of Econometrics, 160, 33–47. DOI: 10.1016/j.jeconom.2010.03.012.
   Web of Science ®Google Scholar
• Zhang, L. (2012), “Implied and Realized Volatility: Empirical Model Selection,” Annals of Finance, 8, 259–275.
   Google Scholar
• Zhang, L., Mykland, P. A., and Aït-Sahalia, Y. (2005), “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data,” Journal of the American Statistical Association, 100, 1394–1411. DOI: 10.1198/016214505000000169.
   Web of Science ®Google Scholar