Exploiting the errors: A simple approach for improved volatility forecasting

We propose a new family of easy-to-implement realized volatility based forecasting models. The models exploit the asymptotic theory for high-frequency realized volatility estimation to improve the accuracy of the forecasts. By allowing the parameters of the models to vary explicitly with the (estimated) degree of measurement error, the models exhibit stronger persistence, and in turn generate more responsive forecasts, when the measurement error is relatively low. Implementing the new class of models for the S&P 500 equity index and the individual constituents of the Dow Jones Industrial Average, we document significant improvements in the accuracy of the resulting forecasts compared to the forecasts from some of the most popular existing models that implicitly ignore the temporal variation in the magnitude of the realized volatility measurement errors.

[1]  Ernst Schaumburg,et al.  Federal Reserve Bank of New York Staff Reports Jump-robust Volatility Estimation Using Nearest Neighbor Truncation Jump-robust Volatility Estimation Using Nearest Neighbor Truncation , 2010 .

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

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

[4]  Jurgen A. Doornik,et al.  Object-orientd matrix programming using OX , 1996 .

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

[6]  F. Diebold,et al.  Financial Risk Measurement for Financial Risk Management , 2011 .

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

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

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

[10]  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.

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

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

[13]  Norman R. Swanson,et al.  Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models , 1997 .

[14]  Nour Meddahi,et al.  Volatility Forecasting when the Noise Variance Is Time-Varying , 2013 .

[15]  Neil Shephard,et al.  Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices , 2012 .

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

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

[18]  Natalia Sizova.  Integrated Variance Forecasting: Model-Based vs. Reduced-Form , 2009 .

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

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

[21]  Neil Shephard,et al.  Measuring Downside Risk - Realised Semivariance , 2008 .

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

[23]  Kevin Sheppard,et al.  Does Anything Beat 5-Minute RV? A Comparison of Realized Measures Across Multiple Asset Classes , 2012 .

[24]  Torben G. Andersen,et al.  Correcting the errors: Volatility forecast evaluation using high-frequency data and realized volatilities , 2005 .

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

[26]  Neil Shephard,et al.  Multivariate High-Frequency-Based Volatility (HEAVY) Models , 2012 .

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

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

[29]  Dacheng Xiu,et al.  Generalized Method of Integrated Moments for High-Frequency Data , 2015 .

[30]  Cecilia Mancini.  Non-parametric Threshold Estimationfor Models with Stochastic DiffusionCoefficient and Jumps , 2006 .

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

[32]  Peter Reinhard Hansen,et al.  REALIZED BETA GARCH: A MULTIVARIATE GARCH MODEL WITH REALIZED MEASURES OF VOLATILITY , 2012 .

[33]  Tim Bollerslev,et al.  Supplementary Appendix to : “ Jump Tails , Extreme Dependencies , and the Distribution of Stock Returns ” ∗ , 2011 .

[34]  Zhou Zhou,et al.  “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data” , 2005 .

[35]  Roxana Halbleib,et al.  Modelling and Forecasting Multivariate Realized Volatility , 2008 .

[36]  Christian Conrad,et al.  The Variance Risk Premium and Fundamental Uncertainty , 2015 .

[37]  Kevin Sheppard,et al.  Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility , 2013, Review of Economics and Statistics.

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

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

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

[41]  John Staudenmayer,et al.  Measurement Error in Linear Autoregressive Models , 2005 .

[42]  Dobrislav Dobrev,et al.  The Information Content of High-Frequency Data for Estimating Equity Return Models and Forecasting Risk , 2010 .

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

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

[45]  Lan Zhang,et al.  A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data , 2003 .

[46]  Andrew J. Patton.  Data-based ranking of realised volatility estimators , 2011 .

[47]  Michael McAleer,et al.  Modelling and Forecasting Noisy Realized Volatility , 2009, Comput. Stat. Data Anal..

[48]  D. Xiu,et al.  Spot Variance Regressions , 2013 .

[49]  Geert Bekaert,et al.  The VIX, the Variance Premium and Stock Market Volatility , 2013, SSRN Electronic Journal.

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

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

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

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

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