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Published online by Cambridge University Press: 24 February 2010
ABSTRACT
In this paper we study the reliability of the mixed normal asymptotic distribution of realized variance error, which we have previously derived using the theory of realized power variation. Our experiments suggest that the asymptotics is reliable when we work with the logarithmic transform of the realized variance.
INTRODUCTION
Tom Rothenberg's outstanding teaching and research has raised the level of understanding econometricians have of the asymptotic properties of estimators and testing procedures used in economics. His frequent trips away from the United States, and his particular kindness to research students during his academic visits, has spread his influence changing the way we carry out theoretical econometric research. This paper touches on some of Tom's research interests. It will look at the effectiveness of an asymptotic theory. His influential paper Rothenberg (1984) was devoted to issues of this type.
The Model
This paper assesses the accuracy of the mixed normal asymptotic approximation to the distribution of realized variance (that is the sum of squares of financial returns) we recently derived in Barndorff-Nielsen and Shephard (2002) and extended in Barndorff-Nielsen and Shephard (2003, 2004). This theory assumes a flexible stochastic volatility (SV) model for log prices.
In the SV model for log prices a basic Brownian motion is generalized to allow the volatility term to vary over time.
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