Abstract: A methodology for nonlinear time series analysis is considered. First, the ideas of (a) added variables in regression analysis and (b) arranged autoregressive fitting in time series analysis are used to propose a proced ure for testing nonlinearity of a univariate time series. The procedure is quite general as compared with other tests available in the literature because it can detect various nonlinearities in a time series such as threshold nonlinearity, bilinearity, and exponential nonlinearity. We then use local estimation in arranged autoregressions to suggest suitable models for a given process. Examples are given to illustrate the proposed methodology.
Key words and phrases: Arranged autoregression, Lagrange multiplier test, local fitting, nonlinear tim e series, predictive residual, threshold model.