COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1597 Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance Peter C.B. Phillips and Jun Yu January 2007 This paper overviews maximum likelihood and Gaussian methods of estimating continuous
time models used in finance. Since the exact likelihood can be constructed only in special
cases, much attention has been devoted to the development of methods designed to
approximate the likelihood. These approaches range from crude Euler-type approximations
and higher order stochastic Taylor series expansions to more complex polynomial-based
expansions and infill approximations to the likelihood based on a continuous time data
record. The methods are discussed, their properties are outlined and their relative finite
sample performance compared in a simulation experiment with the nonlinear CIR diffusion
model, which is popular in empirical finance. Bias correction methods are also considered
and particular attention is given to jackknife and indirect inference estimators. The
latter retains the good asymptotic properties of ML estimation while removing finite
sample bias. This method demonstrates superior performance in finite samples. |
