Parameter Estimation in Mean Reversion Processes with Periodic Functional Tendency

TL;DR

This paper presents a two-phase method for estimating parameters in mean reversion processes with periodic deterministic tendencies, utilizing Fourier series and Gaussian techniques, validated through simulated data experiments.

Contribution

It introduces a novel two-phase estimation procedure combining Fourier series and Gaussian methods for mean reversion processes with periodic tendencies.

Findings

Effective parameter estimation demonstrated on simulated data.

Improved accuracy through iterative reestimation of periodic functional tendency.

Method provides reliable estimates of process parameters and periodic components.

Abstract

This paper describes the procedure to estimate the parameters in mean reversion processes with functional tendency defined by a periodic continuous deterministic function, expressed as a series of truncated Fourier. Two phases of estimation are defined, in the first phase through Gaussian techniques using the Euler-Maruyama discretization, we obtain the maximum likelihood function, that will allow us to find estimators of the external parameters and an estimation of the expected value of the process. In the second phase, a reestimate of the periodic functional tendency with it's parameters of phase and amplitude is carried out, this will allow, improve the initial estimation. Some experimental result using simulated data sets are graphically illustrated.