Time Varying Heteroskedastic Realized GARCH models for tracking measurement error bias in volatility forecasting

Gerlach, Richard and Naimoli, Antonio and Storti, Giuseppe (2018): Time Varying Heteroskedastic Realized GARCH models for tracking measurement error bias in volatility forecasting.

Abstract

This paper proposes generalisations of the Realized GARCH model by Hansen et al. (2012), in three different directions. First, heteroskedasticity in the noise term in the measurement equation is allowed, since this is generally assumed to be time-varying as a function of an estimator of the Integrated Quarticity for intra-daily returns. Second, in order to account for attenuation bias effects, the volatility dynamics are allowed to depend on the accuracy of the realized measure. This is achieved by letting the response coefficient of the lagged realized measure depend on the time-varying variance of the volatility measurement error, thus giving more weight to lagged volatilities when they are more accurately measured. Finally, a further extension is proposed by introducing an additional explanatory variable into the measurement equation, aiming to quantify the bias due to effect of jumps and measurement errors.

• Item Type: MPRA Paper
• Language: English
• Keywords: Realized Volatility, Realized GARCH, Measurement Error, Realized Quarticity
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

References

Andersen, T. G., T. Bollerslev, and F. X. Diebold (2007). Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. The review of economics and statistics 89(4), 701–720.

Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001). The distribution of realized exchange rate volatility. Journal of the American statistical association 96(453), 42–55.

Andersen, T. G., D. Dobrev, and E. Schaumburg (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics 169(1), 75–93.

Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2008). Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica 76(6), 1481–1536.

Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2009). Realized kernels in practice: Trades and quotes. The Econometrics Journal 12(3).

Barndorff-Nielsen, O. E. and N. Shephard (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64(2), 253–280.

Barndorff-Nielsen, O. E. and N. Shephard (2004). Power and bipower variation with stochastic volatility and jumps. Journal of financial econometrics 2(1), 1–37.

Barndorff-Nielsen, O. E. and N. Shephard (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of financial Econometrics 4(1), 1–30.

Bollerslev, T., A. J. Patton, and R. Quaedvlieg (2016). Exploiting the errors: A simple approach for improved volatility forecasting. Journal of Econometrics 192(1), 1–18.

Brownlees, C. T. and G. M. Gallo (2006). Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis 51(4), 2232–2245.

Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 174–196.

Engle, R. (2002). New frontiers for arch models. Journal of Applied Econometrics 17(5), 425–446.

Engle, R. F. and G. M. Gallo (2006). A multiple indicators model for volatility using intra-daily data. Journal of Econometrics 131(1), 3–27.

Hansen, P. and A. Lunde (2011). Forecasting volatility using high frequency data. The Oxford Handbook of Economic Forecasting, Oxford: Blackwell, 525–556.

Hansen, P. R. and Z. Huang (2016). Exponential garch modeling with realized measures of volatility. Journal of Business & Economic Statistics 34(2), 269–287.

Hansen, P. R., Z. Huang, and H. H. Shek (2012). Realized garch: a joint model for returns and realized measures of volatility. Journal of Applied Econometrics 27(6), 877–906.

Hansen, P. R., A. Lunde, and J. M. Nason (2011). The model confidence set. Econometrica 79(2), 453–497.

Huang, X. and G. Tauchen (2005). The relative contribution of jumps to total price variance. Journal of financial econometrics 3(4), 456–499.

Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009). Microstructure noise in the continuous case: the pre-averaging approach. Stochastic processes and their applications 119(7), 2249–2276.

Liu, L. Y., A. J. Patton, and K. Sheppard (2015). Does anything beat 5- minute rv? a comparison of realized measures across multiple asset classes. Journal of Econometrics 187(1), 293–311.

Patton, A., D. N. Politis, and H. White (2009). Correction to "automatic block-length selection for the dependent bootstrap" by D. politis and H. white. Econometric Reviews 28(4), 372–375.

Shephard, N. and K. Sheppard (2010). Realising the future: forecasting with high-frequency-based volatility (heavy) models. Journal of Applied Econometrics 25(2), 197–231.

Shephard, N. and D. Xiu (2016). Econometric analysis of multivariate realised qml: efficient positive semi definite estimators of the covariation of equity prices.

Zhang, L., P. A. Mykland, and Y. Aït-Sahalia (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association 100(472), 1394–1411.