Analysis of Time Series from Switiching Dynamics

Abstract

Suppose that {(x(t),y(t)): t=1,...,T} are generated by m unknown functions. Let r(t) denote the state at time t; that is, r(t)=i if y(t)=f(x(t)) is generated by the i-th function, where i=1,...,m. The task is to determine the m functions and r(t), for t=1,...,T. Pawelzik et al. (1996, Neural Computation) use Neural Networks as competing predictors and adopt an adiabatical annealing method to increase the level of competition. Here we propose to use Support Vector Machines, a new learning technique, as predictors and an EM-like (Expectation Maximization) method to adjust the parameter that controls the level of competition. Advantages of using our approach will be discussed.