Drift estimation for a periodic mean reversion process

Abstract

In this paper we propose a periodic, mean-reverting Ornstein–Uhlenbeck process of the form

$$ dX_t=(L(t)-\alpha\, X_t)\, dt + \sigma\, dB_t, \quad t\geq 0, $$

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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Correspondence to Herold Dehling.

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Dehling, H., Franke, B. & Kott, T. Drift estimation for a periodic mean reversion process. Stat Inference Stoch Process 13, 175–192 (2010). https://doi.org/10.1007/s11203-010-9045-8

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Keywords

  • Time-inhomogeneous diffusion process
  • Ornstein–Uhlenbeck process
  • Maximum likelihood estimation
  • Asymptotic normality