Testing for One-Factor Models versus Stochastic Volatility Models *
Valentina Corradit
Walter Distaso*
University of Exeter
Queen Mary, University of London
November 2004
Abstract
This paper proposes a testing procedure in order to distinguish between the case where the
volatility of an asset price is a deterministic function of the price itself and the one where it
is a function of one or more (possibly unobservable) factors, driven by not perfectly correlated
Brownian motions. Broadly speaking, the objective of the paper is to distinguish between a
generic one-factor model and a generic stochastic volatility model. In fact, no specific assumption
on the functional form of the drift and variance terms is required.
The proposed tests are based on the difference between two different nonparametric estimators
of the integrated volatility process. Building on some recent work by Bandi and Phillips (2003)
and Barndorff-Nielsen and Shephard (2004a), it is shown that the test statistics converge to
a mixed normal distribution under the null hypothesis of a one factor diffusion process, while
diverge in the case of multifactor models. The findings from a Monte Carlo experiment indicate
that the suggested testing procedure has good finite sample properties.
Keywords : realized volatility, stochastic volatility models, one-factor models,
local times, occupation densities, mixed normal distribution
JEL classification: C22, C12, G12.
*We are grateful to Karim Abadir, Carol Alexander, James Davidson, Marcelo Fernandes, Nour Meddahi, Peter
Phillips and the seminar participants to the 2004 SIS conference in Bari, University of Exeter and Universita di
Padova for very helpful comments and suggestions. The authors gratefully acknowledge financial support from the
ESRC, grant code R000230006.
tQueen Mary, University of London, Department of Economics, Mile End, London, E14NS, UK, email:
[email protected].
* University of Exeter, Department of Economics, Streatham Court, Exeter EX4 4PU, UK, email:
[email protected].