Hark the Shark: Realized Volatility Modelling with Measurement Errors and Nonlinear Dependencies

Despite their effectiveness, linear models for realized variance neglect measurement errors on integrated variance and exhibit several forms of misspecification due to the inherent nonlinear dynamics of volatility. We propose new extensions of the popular approximate long-memory HAR model apt to disentangle these effects and quantify their separate impact on volatility forecasts. By combining the asymptotic theory of the realized variance estimator with the Kalman filter and by introducing time-varying HAR parameters, we build new models that account for: (i) measurement errors (HARK), (ii) nonlinear dependencies (SHAR) and (iii) both measurement errors and nonlinearities (SHARK). The proposed models are simply estimated through standard maximum likelihood methods and are shown, both on simulated and real data, to provide better out-of-sample forecasts compared to standard HAR specifications and other competing approaches.

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

[2]  Roberto Renò,et al.  Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling , 2010 .

[3]  Tim Bollerslev,et al.  Exploiting the errors: A simple approach for improved volatility forecasting , 2016 .

[4]  Andre Lucas,et al.  Research Unit for Statistical and Empirical Analysis in Social Sciences (hi-stat) Global Coe Hi-stat Discussion Paper Series a General Framework for Observation Driven Time-varying Parameter Models a General Framework for Observation Driven Time-varying Parameter Models * , 2022 .

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

[6]  R. Engle,et al.  A Multiple Indicators Model for Volatility Using Intra-Daily Data , 2003 .

[7]  Piotr Cofta,et al.  The Model of Confidence , 2007 .

[8]  R. Engle.  New Frontiers for Arch Models , 2002 .

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

[10]  Rogier Quaedvlieg,et al.  Multi-Horizon Forecast Comparison , 2018, Journal of Business & Economic Statistics.

[11]  Siem Jan Koopman,et al.  Observation-Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk , 2011, Review of Economics and Statistics.

[12]  Dan Simon.  Kalman filter generalizations , 2006 .

[13]  Wolfgang Härdle,et al.  Localized Realized Volatility Modeling , 2010 .

[14]  Tim Bollerslev,et al.  Modeling and Forecasting (Un)Reliable Realized Covariances for More Reliable Financial Decisions , 2016, Journal of Econometrics.

[15]  E. Otranto,et al.  On Heteroskedasticity and Regimes in Volatility Forecasting , 2017 .

[16]  S. Mittnik,et al.  The Volatility of Realized Volatility , 2005 .

[17]  Leonidas S. Rompolis,et al.  Forecasting the mean and volatility of stock returns from option prices , 2006 .

[18]  Ivan Petrella,et al.  Adaptive State Space Models with Applications to the Business Cycle and Financial Stress , 2016 .

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

[20]  Drew D. Creal,et al.  Generalized autoregressive score models with applications ∗ , 2010 .

[21]  A. Hall.  DYNAMIC MODELS FOR VOLATILITY AND HEAVY TAILS: WITH APPLICATIONS TO FINANCIAL AND ECONOMIC TIME SERIES, BY A. C. HARVEY. PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS, 2013 NEW YORK, USA. TOTAL NUMBER OF PAGES: 261. PRICE: $36.99. ISBN: 978‐1‐107‐63002‐4 , 2014 .

[22]  A. Harvey.  Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series , 2013 .

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

[24]  Fulvio Corsi,et al.  Realizing Smiles: Options Pricing with Realized Volatility , 2011 .

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

[26]  Jiti Gao,et al.  Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models , 2018 .

[27]  T. Wansbeek.  Measurement error and latent variables in econometrics , 2000 .

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

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

[30]  M. Medeiros,et al.  A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries , 2008 .

[31]  James Durbin,et al.  Time Series Analysis by State Space Methods: Second Edition , 2012 .

[32]  F. Blasques,et al.  Optimal Formulations for Nonlinear Autoregressive Processes , 2014 .