Modeling non-stationary stochastic systems with generalized time series models

This paper focuses on the modeling problems for the discrete-time stochastic system, whose probabilistic characteristics, like mean and variance, are time-varying. By using the linear or non-linear Kalman type filters, state-space models can be used to model such systems. However, the number of the unknown parameters of the state-space models monotonously increase along with time. To make modeling and further applications more convenient, we propose a generalized time series (GTS) model for the non-stationary stochastic models by combining the generalized additive model with location, scale and shape and autoregressive models with exogenous variables. GTS is in fact a kind of parametric models, which can predict the time varying probability distribution characteristics. Meanwhile, GTS is not limited to the Gaussian distribution. To evaluate the estimated GTS models, we use the Bayesian information criterion (BIC). Furthermore, we propose a BIC-based hierarchical selection algorithm to investigate the optimal structures for GTS. Finally, we use the real data of distribution storm time to illustrated the applicability and effectiveness of the proposed GTS model and methods.