Correcting Intraday Periodicity Bias in Realized Volatility Measures

Abstract Diurnal fluctuations in volatility are a well-documented stylized fact of intraday price data. This warrants an investigation how this intraday periodicity (IP) affects both finite sample as well as asymptotic properties of several popular realized estimators of daily integrated volatility which are based on functionals of a finite number of intraday returns. It turns out that most of the estimators considered in this study exhibit a finite-sample bias due to IP, which can however get negligible when the number of intraday returns diverges to infinity. The appropriate correction factors for this bias are derived based on estimates of the IP. The adequacy of the new corrections is evaluated by means of a Monte Carlo simulation study and an empirical example.

[1]  J. Ord,et al.  An Investigation of Transactions Data for NYSE Stocks , 1985 .

[2]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[3]  M. Izzeldin,et al.  Forecasting the Realized Variance in the Presence of Intraday Periodicity , 2019, SSRN Electronic Journal.

[4]  N. Shephard,et al.  Realized Kernels in Practice: Trades and Quotes , 2009 .

[5]  Ernst Schaumburg,et al.  A ROBUST NEIGHBORHOOD TRUNCATION APPROACH TO ESTIMATION OF INTEGRATED QUARTICITY , 2013, Econometric Theory.

[6]  Stephen L Taylor,et al.  The incremental volatility information in one million foreign exchange quotations , 1997 .

[7]  T. Bollerslev,et al.  Intraday periodicity and volatility persistence in financial markets , 1997 .

[8]  Jean Jacod,et al.  Discretization of Processes , 2011 .

[9]  Torben G. Andersen,et al.  No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications , 2007 .

[10]  Mark Podolskij,et al.  Fact or Friction: Jumps at Ultra High Frequency , 2014 .

[11]  W. Schmid,et al.  Statistical inferences for realized portfolio weights , 2020 .

[12]  Roel C. A. Oomen,et al.  Realised quantile-based estimation of the integrated variance , 2010 .

[13]  T. Andersen,et al.  Time-Varying Periodicity in Intraday Volatility , 2019, Journal of the American Statistical Association.

[14]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[15]  Anat R. Admati,et al.  A Theory of Intraday Patterns: Volume and Price Variability , 1988 .

[16]  Neil Shephard,et al.  Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise , 2008 .

[17]  H. Dette,et al.  The effect of intraday periodicity on realized volatility measures , 2022, Metrika.

[18]  P. Kokoszka,et al.  Monitoring the Intraday Volatility Pattern , 2013 .

[19]  Vasyl Golosnoy,et al.  Intra-daily volatility spillovers in international stock markets , 2015 .

[20]  Christophe Croux,et al.  Robust Estimation of Intraweek Periodicity in Volatility and Jump Detection , 2008 .

[21]  Jeremias Bekierman,et al.  A Mixed Frequency Stochastic Volatility Model for Intraday Stock Market Returns , 2019 .

[22]  Ashish Das,et al.  Variance‐ratio Statistics and High‐frequency Data: Testing for Changes in Intraday Volatility Patterns , 2001 .

[23]  Wolfgang Schmid,et al.  CUSUM control charts for monitoring optimal portfolio weights , 2011, Comput. Stat. Data Anal..

[24]  Exponential smoothing of realized portfolio weights , 2019, Journal of Empirical Finance.

[25]  Jean Jacod,et al.  Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 , 2007 .

[26]  G. Buccheri,et al.  HARK the SHARK: Realized Volatility Modeling with Measurement Errors and Nonlinear Dependencies* , 2019, Journal of Financial Econometrics.

[27]  Kim Christensen,et al.  Is the Diurnal Pattern Sufficient to Explain Intraday Variation In Volatility? A Nonparametric Assessment , 2017, Journal of Econometrics.

[28]  C. Klüppelberg,et al.  Financial risk measures for a network of individual agents holding portfolios of light-tailed objects , 2019, Finance and Stochastics.

[29]  Oliver Kley,et al.  Conditional risk measures in a bipartite market structure , 2015, 1510.00616.

[30]  L. Harris.  A transaction data study of weekly and intradaily patterns in stock returns , 1986 .

[31]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[32]  Giuseppe Buccheri,et al.  Hark the Shark: Realized Volatility Modelling with Measurement Errors and Nonlinear Dependencies , 2019 .

[33]  N. Shephard,et al.  Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise , 2006 .