title: Empirical Fokker-Planck-based test of stationarity for time series.
abstract: We propose a test of stationarity based on the drift coefficients of the Langevin type and the associated Fokker-Planck equations. The test relies on the estimation of the drift coefficients of the underlying probability densities and posits that a time series is nonstationary if the estimated drift term is a nonlinear function of the random variable of the observed time series and the Markov property holds. We provide ample empirical evidence that demonstrates that well- known stationary systems give rise to linear estimates of the drift coefficients, whereas nonstationary time series exhibit nonlinear estimates of the drift term. This does not, indeed, imply that a nonlinear drift term in the Fokker-Planck equation of a dynamic stochastic process causes nonstationarity.
authors.affiliation: Department of Chemistry and Physics, The University of Tennessee at Martin, Martin, Tennessee 38238, USA.
authors.forename: Cahit
authors.initials: C
authors.lastname: Erkal
authors.affiliation: Department of Economics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA.
authors.forename: Aydin A
authors.initials: AA
authors.lastname: Cecen
mesh_terms: D004058:Diffusion; D006339:Heart Rate; D006801:Humans; D016014:Linear Models; D008390:Markov Chains; D017059:Models, Econometric; D017711:Nonlinear Dynamics; D012044:Regression Analysis; D013269:Stochastic Processes; D013995:Time