Detection of hidden regimes in stochastic cyclostationary time series

Stationary stochastic time series with nonlinear dynamics can feature a probability density function (PDF) with distinct local maxima associated with distinct regimes. For nonstationary time series, on the other hand, such regimes are not necessarily reflected in the shape of the PDF. This occurs when the duration of a regime is too short for the PDF to adjust, and such a regime is called a "hidden" regime. This paper presents an algorithm that allows one to detect hidden regimes in cyclostationary stochastic Markovian time series. The method involves analysis of an appropriately windowed time series, from which the drift and diffusion coefficients of the associated Fokker-Planck equation are estimated. The success of the algorithm is illustrated using synthetic time series with both additive and multiplicative noise.