WORKING PAPERS SERIES
Estimating and Testing Stochastic
Volatility Models using Realized Measures
Valentina Corradi and Walter Distaso
Estimating and Testing Stochastic Volatility Models using Realized
Queen Mary, University of London
University of Exeter
This paper proposes a procedure to test for the correct specification of the functional form of the
volatility process, within the class of eigenfunction stochastic volatility models (Meddahi, 2001).
The procedure is based on the comparison of the moments of realized volatility measures with
the corresponding ones of integrated volatility implied by the model under the null hypothesis.
We first provide primitive conditions on the measurement error associated with the realized
measure, which allow to construct asymptotically valid specification tests.
Then we establish regularity conditions under which realized volatility, bipower variation (Barndor!-
Nielsen & Shephard, 2004d), and modified subsampled realized volatility (Zhang, Mykland &
Aı̈t Sahalia, 2003), satisfy the given primitive assumptions.
Finally, we provide an empirical illustration based on three stock from the Dow Jones Industrial
generalized method of moments, eigenfunction stochastic volatility model,
integrated volatility, jumps, realized volatility, bipower variation,
JEL classification: C22, C12, G12.
!We wish to thank the editor, Bernard Salanié, two anonymous referees, and Karim Abadir, Andrew Chesher,
Atsushi Inoue, Paul Labys, Oliver Linton, Enrique Sentana, Ron Smith, as well as the seminar participants at the
2003 Winter meeting of Econometric Society in Washington DC, the 2003 Forecasting Financial Markets Conference
in Paris, the 2003 Money, Macro and Finance Conference at London Metropolitan University, LSE-Financial Market
Group, the 2003 CIREQ-CIRANO Realized Volatility Conference at University of Montreal, IFS-UCL, Rutgers
University and Università di