Data-based ranking of realised volatility estimators

This paper presents new methods for comparing the accuracy of estimators of the quadratic variation of a price process. I provide conditions under which the relative accuracy of competing estimators can be consistently estimated (as T-->[infinity]), and show that forecast evaluation tests may be adapted to the problem of ranking these estimators. The proposed methods avoid making specific assumptions about microstructure noise, and facilitate comparisons of estimators that would be difficult using methods from the extant literature, such as those based on different sampling schemes. An application to high frequency IBM data between 1996 and 2007 illustrates the new methods.

[1]  Estimating Quadratic Variation Consistently in the Presence of Correlated Measurement Error , 2006 .

[2]  Robert F. Engle,et al.  The Econometrics of Ultra-High Frequency Data , 1996 .

[3]  Bin Zhou,et al.  High Frequency Data and Volatility in Foreign Exchange Rates , 2013 .

[4]  P. Hansen,et al.  A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data , 2005 .

[5]  Kim Christensen,et al.  Realized Range-Based Estimation of Integrated Variance , 2006 .

[6]  Richard A. Davis,et al.  Handbook of Financial Time Series , 2009 .

[7]  Kevin Sheppard,et al.  Evaluating Volatility and Correlation Forecasts , 2009 .

[8]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[9]  George Tauchen,et al.  Realized Jumps on Financial Markets and Predicting Credit Spreads , 2006 .

[10]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[11]  Halbert White,et al.  Tests of Conditional Predictive Ability , 2003 .

[12]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[13]  Maureen O'Hara,et al.  Time and the Process of Security Price Adjustment , 1992 .

[14]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[15]  Torsten Persson,et al.  Advances in economics and econometrics : theory and applications, Ninth World Congress , 2006 .

[16]  Nour Meddahi,et al.  BOOTSTRAPPING REALIZED VOLATILITY , 2009 .

[17]  Clive W. J. Granger.  Outline of forecast theory using generalized cost functions , 1999 .

[18]  Kevin Sheppard,et al.  Optimal combinations of realised volatility estimators , 2009 .

[19]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[20]  D. Steigerwald,et al.  Noise reduced realized volatility: a kalman filter approach , 2009 .

[21]  P. Burridge,et al.  A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix , 1991 .

[22]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[23]  Thomas B. Fomby,et al.  Econometric analysis of financial and economic time series , 2006 .

[24]  S. Manganelli.  Duration, Volume and Volatility Impact of Trades , 2002, SSRN Electronic Journal.

[25]  K. French,et al.  Expected stock returns and volatility , 1987 .

[26]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

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

[28]  P. Hansen,et al.  ESTIMATING THE PERSISTENCE AND THE AUTOCORRELATION FUNCTION OF A TIME SERIES THAT IS MEASURED WITH ERROR , 2010, Econometric Theory.

[29]  Chris Kirby,et al.  The Economic Value of Volatility Timing , 2000 .

[30]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[31]  Tim Bollerslev,et al.  Volatility and Time Series Econometrics , 2010 .

[32]  Ioanid Roşu.  Graduate School of Business University of Chicago , 2005 .

[33]  Andrew J. Patton,et al.  Generalized Forecast Errors, A Change of Measure, and Forecast Optimality , 2008 .

[34]  T. Bollerslev,et al.  Analytical Evaluation of Volatility Forecasts , 2002 .

[35]  N. Meddahi,et al.  ARMA representation of integrated and realized variances , 2003 .

[36]  Michael McAleer,et al.  Realized Volatility and Long Memory: An Overview , 2008 .

[37]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[38]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[39]  Yacine Ait-Sahalia,et al.  Out of Sample Forecasts of Quadratic Variation , 2008 .

[40]  Dean P. Foster,et al.  Continuous Record Asymptotics for Rolling Sample Variance Estimators , 1994 .

[41]  James J. Heckman,et al.  Handbook of Econometrics , 1985 .

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

[43]  P. Hansen.  A Test for Superior Predictive Ability , 2005 .

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

[45]  F. Diebold,et al.  Chapter 15 Volatility and Correlation Forecasting , 2006 .

[46]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[47]  F. Diebold,et al.  Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility , 2005, The Review of Economics and Statistics.

[48]  Estimating quadratic variation when quoted prices change by a constant increment , 2011 .

[49]  D. Dijk,et al.  Measuring volatility with the realized range , 2006 .

[50]  R. Oomen.  Properties of Realized Variance Under Alternative Sampling Schemes , 2006 .

[51]  F. Vega-Redondo.  Complex Social Networks: Econometric Society Monographs , 2007 .

[52]  Lan Zhang.  Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach , 2004, math/0411397.

[53]  T. Bollerslev,et al.  A Reduced Form Framework for Modeling Volatility of Speculative Prices Based on Realized Variation Measures , 2008 .

[54]  Oliver Linton,et al.  Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error , 2008 .

[55]  Jonathan H. Wright.  Testing for a Unit Root in the Volatility of Asset Returns , 1999 .

[56]  P. Hansen,et al.  A Forecast Comparison of Volatility Models: Does Anything Beat a Garch(1,1)? , 2004 .

[57]  Siem Jan Koopman,et al.  State Space and Unobserved Component Models: Theory and Applications , 2004 .

[58]  P. Hansen,et al.  Realized Variance and Market Microstructure Noise , 2005 .

[59]  Yacine Ait-Sahalia,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[60]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[61]  Peter Reinhard Hansen,et al.  The Model Confidence Set , 2010 .

[62]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[63]  N. Shephard,et al.  State Space and Unobserved Component Models: Measuring and forecasting financial variability using realised variance , 2004 .

[64]  Jeffrey R. Russell,et al.  Separating Microstructure Noise from Volatility , 2004 .

[65]  Jim Gatheral,et al.  Zero-intelligence realized variance estimation , 2009, Finance Stochastics.

[66]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[67]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[68]  Hong Zhang,et al.  Forecasting Volatility in Financial Markets , 2010 .

[69]  H. White.  Asymptotic theory for econometricians , 1985 .

[70]  Asger Lunde,et al.  Realized Variance and Market Microstructure Noise , 2006 .

[71]  N. Shephard,et al.  Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation , 2005 .

[72]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

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

[74]  E. Ghysels,et al.  Volatility Forecasting and Microstructure Noise , 2006 .

[75]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

[76]  Andrew J. Patton,et al.  What good is a volatility model? , 2001 .

[77]  C. Granger,et al.  Forecasting Volatility in Financial Markets: A Review , 2003 .

[78]  Federico M. Bandi,et al.  Microstructure Noise, Realized Variance, and Optimal Sampling , 2008 .

[79]  Michael Wolf,et al.  Centre De Referència En Economia Analítica Barcelona Economics Working Paper Series Working Paper Nº 17 Stewise Multiple Testing as Formalized Data Snooping Stepwise Multiple Testing as Formalized Data Snooping , 2022 .

[80]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[81]  Jeffrey R. Russell,et al.  Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations , 2011 .

[82]  H. White,et al.  A Reality Check for Data Snooping , 2000 .

[83]  Andrew J. Patton.  Volatility Forecast Comparison Using Imperfect Volatility Proxies , 2006 .

[84]  P. Hansen,et al.  Consistent Ranking of Volatility Models , 2006 .

[85]  Andrew J. Patton,et al.  Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity , 2007 .

[86]  Jeremy H. Large.  Estimating Quadratic Variation When Quoted Prices Change by a Constant Increment , 2007 .

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

[88]  N. Shephard,et al.  Variation, Jumps, Market Frictions and High Frequency Data in Financial Econometrics , 2005 .

[89]  Chen Yang,et al.  Realized Volatility Forecasting in the Presence of Time-Varying Noise , 2013 .

[90]  Michael A. Salsburg,et al.  Modeling and Forecasting , 2007, Int. CMG Conference.

[91]  T. Bollerslev,et al.  Realized volatility forecasting and market microstructure noise , 2011 .

[92]  Measuring and forecasting financial variability using realised variance with and without a model , 2002 .

[93]  Huimin Chung,et al.  Estimation of GARCH Models from the Autocorrelations of the Squares of a Process , 2001 .

[94]  George Tauchen,et al.  Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance , 2012 .

[95]  F. Diebold,et al.  VOLATILITY AND CORRELATION FORECASTING , 2006 .