Reasoning about non-linear autoregressive models using expectation maximization

A simplified version of the expectation maximization (EM) algorithm is applied to search for optimal state sequences in state-dependent AR models whereby no prior knowledge about the state equation is necessary. These sequences can be used to draw conclusions about functional dependencies between the observed process and estimated AR coefficients. Consequently this approach is especially helpful in the identification of functional-coefficient AR models where the coefficients are controlled by the process itself. The approximation of regression functions in first-order non-linear AR models and the localization of multiple thresholds in self-exciting threshold autoregressive models are demonstrated as examples.