ABSTRACT
This chapter provides the need for non-linear models and attempts the difficult task of distinguishing between linear and non-linear models. Non-linear models are needed to describe data where the variance changes through time. Non-linear models can also be used to explain, and give forecasts for, data exhibiting regular cyclic behaviour. For some non-linear models, if the noise process is ‘switched off’, then the process will converge asymptotically to a strictly periodic form called a limit cycle. In much of statistical methodology, the term general linear modelgeneral linear modelnon-linear model is used to describe a model that is linear in the parameters but that could well involve non-linear functions of the explanatory variables in the so-called design matrix. A non-linear model could be defined by exclusion as any model that is not linear. When examining the properties of non-linear models, it can be very important to distinguish between independent and uncorrelated random variables.
