Complutense University Library

Modelling and Forecasting Noisy Realized Volatility


Asai, Manabu and McAleer, Michael and Medeiros, Marcelo C. (2011) Modelling and Forecasting Noisy Realized Volatility. [ Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 09, 2011, ] (Submitted)

Creative Commons Attribution Non-commercial.


Official URL:


Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. As such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected 2R recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of
2 R . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper.

Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Realized volatility; Diffusion; Financial econometrics; Measurement errors; Forecasting; Model evaluation; Goodness-of-fit.
Subjects:Social sciences > Economics > Finance
Social sciences > Economics > Econometrics
Series Name:Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE)
ID Code:12562

Andersen, T.G.. and T. Bollerslev (1998), “Answering the skeptics: Yes, standard volatility models do provide accurate forecasts”, International Economic Review, 39, 885 – 905.

Andersen, T., T. Bollerslev, F.X. Diebold and H. Ebens (2001), “The distribution of realized stock return volatility”, Journal of Financial Economics, 61, 43–76.

Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (2003), “Modeling and forecasting realized volatility”, Econometrica, 71, 529 – 626.

Andersen, T., T. Bollerslev and N. Meddahi (2005), “Correcting the errors: A note on volatility forecast evaluation based on high-frequency data and realized volatilities,” Econometrica, 73, 279 – 296.

Asai, M. (2008), “Autoregressive stochastic volatility models with heavy-tailed distribution: A comparison with multifactor volatility models”, Journal of Empirical Finance, 15, 332-341.

Asai, M., M. McAleer and J. Yu (2006), “Multivariate stochastic volatility: A review”, Econometric Reviews, 25, 145 – 175.

Bandi, F.M. and J.R. Russell (2007), “Volatility estimation”, In J. Birge and V. Linetsky eds., Handbook in Operations Research and Management Science: Financial Engineering, North Holland, Elsevier, 183-222.

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, 64, 253-280.

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

Bollerslev, T. (1986), “Generalized autoregressive conditional heteroskedasticity”, Journal of Econometrics, 21, 307 – 328.

Breidt, F.J., N. Crato and P.J.F. de Lima (1998), “The detection and estimation of long-memory in stochastic volatility”, Journal of Econometrics, 83, 325 – 348.

Chernov, M., A.R. Gallant, E. Ghysels and G. Tauchen (2003), “Alternative models for stock price dynamics”, Journal of Econometrics, 116, 225 – 257.

Corradi, V. and W. Distaso (2006), “Semiparametric comparison of stochastic volatility models using realized measures”, Review of Economic Studies, 73, 635-677.

Corsi, F. (2009), “A simple approximate long memory model of realized volatility,” Journal of Financial Econometrics, 7, 174-196.

Engle, R.F. (1982), “Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation”, Econometrica, 50, 987-1007.

Ghysels, E., A.C. Harvey and E. Renault (1996), “Stochastic volatility”, In C. R.Rao and G. S. Maddala eds., Statistical Methods in Finance, pp.119-191. Amsterdam: North-Holland.

Hansen, P.R., J. Large and A. Lunde (2008), “Moving average-based estimators of integrated variance”, Econometric Reviews, 27, 79-111.

Hansen, P.R. and A. Lunde (2006), “Realized variance and market microstructure noise” (with discussion), Journal of Business and Economic Statistics, 24, 127 – 218.

Harvey, A.C. (1998), “Long memory in stochastic volatility”, in J. Knight and E. Satchell (eds.), Forecasting Volatility in Financial Markets, Butterworth–Haineman, London, pp. 307–320.

Harvey, A. C. and N. Shephard (1996), “Estimation of an asymmetric stochastic volatility model for asset returns”, Journal of Business and Economic Statistics, 14, 429-34.

Kitagawa, G. (1987), “Non-Gaussian state-space modeling of nonstationary time series,” Journal of the American Statistical Association, 82, 1032-1063 (with discussion).

McAleer, M. (2005), “Automated inference and learning in modeling financial volatility”, Econometric Theory, 21, 232 – 261.

McAleer, M. and M. Medeiros (2008a), “Realized volatility: A review”, Econometric Reviews, 27, 10-45.

Meddahi, N. (2002), “A theoretical comparison between integrated and realized volatility”, Journal of Applied Econometrics, 17, 479 – 508.

Nelson, D. B. (1990), “ARCH models as diffusion approximations”, Journal of Econometrics, 45, 7–38.

Nelson, D. B. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, 59, 347-70.

So, M.K.P. (1999), “Time series with additive noise”, Biometrika, 86, 474-482.

Tanaka, K. (2002), “A unified approach to the measurement error problem in time series models”, Econometric Theory, 18, 278 – 296.

Taylor, S.J. (1986), Modelling Financial Time Series, Wiley, Chichester.

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, 1394 – 1411.

Deposited On:11 Apr 2011 08:52
Last Modified:14 Mar 2014 08:55

Repository Staff Only: item control page