Bayesian Nonparametric Estimation of Ex-post Variance

Griffin, Jim and Liu, Jia and Maheu, John M (2016): Bayesian Nonparametric Estimation of Ex-post Variance.

Abstract

Variance estimation is central to many questions in finance and economics. Until now ex-post variance estimation has been based on infill asymptotic assumptions that exploit high-frequency data. This paper offers a new exact finite sample approach to estimating ex-post variance using Bayesian nonparametric methods. In contrast to the classical counterpart, the proposed method exploits pooling over high-frequency observations with similar variances. Bayesian nonparametric variance estimators under no noise, heteroskedastic and serially correlated microstructure noise are introduced and discussed. Monte Carlo simulation results show that the proposed approach can increase the accuracy of variance estimation. Applications to equity data and comparison with realized variance and realized kernel estimators are included.

• Item Type: MPRA Paper
• Language: English
• Keywords: pooling, microstructure noise, slice sampling
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; 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 > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets

References

Aı̈t-Sahalia, Y. & Jacod, J. (2014), High-Frequency Financial Econometrics, Princeton University Press.

Aı̈t-Sahalia, Y. & Mancini, L. (2008), ‘Out of sample forecasts of quadratic variation’, Journal of Econometrics 147(1), 17–33.

Aı̈t-Sahalia, Y., Mykland, P. A. & Zhang, L. (2011), ‘Ultra high frequency volatility estimation with dependent microstructure noise’, Journal of Econometrics 160(1), 160-175.

Andersen, T. & Bollerslev, T. (1998), ‘Answering the skeptics: Yes, standard volatility models do provide accurate forecasts’, International Economic Review 39(4), 885–905.

Andersen, T. G. & Benzoni, L. (2008), Realized volatility, Working Paper Series WP-08-14, Federal Reserve Bank of Chicago. URL: https://ideas.repec.org/p/fip/fedhwp/wp-08-14.html

Andersen, T. G., Bollerslev, T., Diebold, F. X. & Ebens, H. (2001), ‘The distribution of realized stock return volatility’, Journal of Financial Economics 61(1), 43–76.

Andersen, T. G., Bollerslev, T., Diebold, F. X. & Labys, P. (2001), ‘The Distribution of Realized Exchange Rate Volatility’, Journal of the American Statistical Association 96, 42–55.

Andersen, T. G., Bollerslev, T., Diebold, F. X. & Labys, P. (2003), ‘Modeling and Forecasting Realized Volatility’, Econometrica 71(2), 579–625.

Andersen, T. G., Bollerslev, T. & Meddahi, N. (2011), ‘Realized volatility forecasting and market microstructure noise’, Journal of Econometrics 160(1), 220–234.

Bandi, F. M. & Russell, J. R. (2008), ‘Microstructure noise, realized variance, and optimal sampling’, The Review of Economic Studies 75(2), 339–369.

Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A. & Shephard, N. (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., Hansen, P. R., Lunde, A. & Shephard, N. (2009), ‘Realized kernels in practice: trades and quotes’, Econometrics Journal 12(3), 1–32.

Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A. & Shephard, N. (2011), ‘Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading’, Journal of Econometrics 162(2), 149–169.

Barndorff-Nielsen, O. E. & Shephard, N. (2002), ‘Estimating quadratic variation using realized variance’, Journal of Applied Econometrics 17, 457–477.

Barndorff-Nielsen, O. E. & Shephard, N. (2006), ‘Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation’, Journal of Financial Econometrics 4(1), 1–30.

Bollen, B. & Inder, B. (2002), ‘Estimating daily volatility in financial markets utilizing intraday data’, Journal of Empirical Finance 9(5), 551–562.

Bollerslev, T., Patton, A. & Quaedvlieg, R. (2016), ‘Exploiting the errors: A simple approach for improved volatility forecasting’, Journal of Econometrics 192, 1–18.

Chernov, M., Ronald Gallant, A., Ghysels, E. & Tauchen, G. (2003), ‘Alternative models for stock price dynamics’, Journal of Econometrics 116(1-2), 225–257.

Corradi, V., Distaso, W. & Swanson, N. R. (2009), ‘Predictive density estimators for daily volatility based on the use of realized measures’, Journal of Econometrics 150(2), 119–138.

Corsi, F. (2009), ‘A Simple Approximate Long-Memory Model of Realized Volatility’, Journal of Financial Econometrics 7(2), 174–196.

Escobar, M. D. & West, M. (1994), ‘Bayesian Density Estimation and Inference Using Mixtures’, Journal of the American Statistical Association 90, 577–588.

Ferguson, T. S. (1973), ‘A Bayesian analysis of some nonparametric problems’, The Annals of Statistics 1(2), 209–230.

Goncalves, S. & Meddahi, N. (2009), ‘Bootstrapping realized volatility’, Econometrica 77(1), 283–306.

Hansen, P., Large, J. & Lunde, A. (2008), ‘Moving Average-Based Estimators of Integrated Variance’, Econometric Reviews 27(1-3), 79–111.

Hansen, P. R. & Lunde, A. (2006), ‘Realized Variance and Market Microstructure Noise’, Journal of Business & Economic Statistics 24, 127–161.

Huang, X. & Tauchen, G. (2005), ‘The Relative Contribution of Jumps to Total Price Variance’, Journal of Financial Econometrics 3(4), 456–499.

Kalli, M., Griffin, J. E. & Walker, S. G. (2011), ‘Slice sampling mixture models’, Statistics and Computing 21(1), 93–105.

Maheu, J. M. & McCurdy, T. H. (2002), ‘Nonlinear Features of Realized FX Volatility’, The Review of Economics and Statistics 84(4), 668–681.

Neal, R. M. (2000), ‘Markov chain sampling methods for Dirichlet Process mixture models’, Journal of Computational and Graphical Statistics 9(2), 249–265.

Sethuraman, J. (1994), ‘A constructive definition of Dirichlet priors’, Statistica Sinica pp. 639–650.

Zhang, L., Mykland, P. A. & Aı̈t-Sahalia, Y. (2005), ‘A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data’, Journal of the American Statistical Association 100, 1394–1411.

Zhou, B. (1996), ‘High frequency data and volatility in foreign exchange rates’, Journal of Business and Economic Statistics 14(1), 45–52.