Drift estimation for a periodic mean reversion process
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Date
2010-05-25T12:17:45Z
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Abstract
In this paper we propose a periodic, mean-reverting Ornstein-Uhlenbeck process
of the form
dXt = (L(t) − alpha Xt) dt + sigma dBt,
where L(t) is a periodic, parametric function. We apply maximum likelihood estimation
for the drift parameters based on time-continuous observations. The estimator is given
explicitly and we prove strong consistency and asymptotic normality as the observed number
of periods tends to infinity. The essential idea of the asymptotic study is the interpretation
of the stochastic process as a sequence of random variables that take values in some function
space.
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Keywords
Asymptotic normality, Maximum likelihood estimation, Ornstein-Uhlenbeck process, Time-inhomogeneous diffusion process