A nonlinear approach to modeling climatological time series

Autoregressive moving average (ARMA) processes are frequently used to model climatological time series. These tools form a broad segment of the class of linear stochastic processes. This paper summarizes formulation of nonlinear models and gives a review of a best developed type of nonlinearity. The main steps of model fitting, i.e. test for nonlinearity, model estimation, and model checking are described. The methodology is applied to Central England annual mean temperature data. A threshold autoregressive model, a piecewise constant approximation to nonlinearity, delivers a statistically significant gain over the best fitting AR model. The forecasting function has three stable points and one limit cycle related to quasi-biennial oscillation.