Abstract
A distinction is made between serial uncorrelatedness and independence, which leads to the concept of a martingale, this being a generalized random walk. This in turn leads to the consideration of nonlinear stochastic processes for generating time series. Several nonlinear models are introduced that have found application in a variety of fields: the bilinear model, threshold and smooth autoregressions, Markov-switching models, neural networks, and chaotic processes. Given the wide range of nonlinear processes available, testing for nonlinearity is paramount and many tests with power against one or more nonlinear alternatives have been proposed. The complexities of forecasting nonlinear processes are also briefly discussed.
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