Transient dynamics of non-linear models describing multi-stable stochastic systems

Multi-stable stochastic systems are inherently nonlinear and typically have long transient times before stationary state is reached. Black-box dynamic models always assume the data to be from a stationary system. In this paper, we discuss a method to assess whether data is long enough to justify non-linear time series model. Our method discretizes state space and studies the corresponding Markov chain. The eigenvalues of the Markov transition operator provide leading transient time constants. The method is illustrated by generating data with a known multi-stable model and then analyzing the data with NNAR(1) and polynomial lag-1 time series model.