The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures

48 Pages Posted: 20 Sep 2011 Last revised: 10 Sep 2012

See all articles by Siem Jan Koopman

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Marcel Scharth

The University of Sydney

Date Written: September 20, 2011

Abstract

We develop a systematic framework for the joint modelling of returns and multiple daily realised measures. We assume a linear state space representation for the log realised measures, which are noisy and biased estimates of the log daily integrated variance, at least due to Jensen's inequality. We incorporate filtering methods for the estimation of the latent log volatility process. The dependence between daily returns and realised measurement errors leads us to develop a two-step estimation method for all parameters in our model specification. The estimation method is computationally straightforward even when the stochastic volatility model has non-Gaussian return innovations and leverage effects. Our extensive empirical study for nine Dow Jones stock return series reveals that measurement errors become significantly smaller after filtering and that the forecasts from our model outperforms those from a set of recently developed alternatives.

Keywords: Kalman filter, leverage, realised volatility, simulated maximum likelihood

JEL Classification: C22, C58

Suggested Citation

Koopman, Siem Jan and Scharth, Marcel, The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures (September 20, 2011). Available at SSRN: https://ssrn.com/abstract=1930932 or http://dx.doi.org/10.2139/ssrn.1930932

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Marcel Scharth (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

HOME PAGE: http://www.marcelscharth.com

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