Time series: The values of a variable recorded, generally at a regular interval, over the long period of time.

The observed movement and fluctuations of several such series are composed of four diverse components, seasonal variation, secular trend, cyclical variation, and the irregular variation. An instance from medicine is the incidence of the disease recorded yearly over several decades. Such type of data usually needs special methods for their analysis because of presence of the serial correlation between separate observations. Most often time series are analyzed by the linear models such the classic family of the autoregressive moving average models.

But there are number of observable phenomena which cannot be accounted for adequately by the linear models and which give rise to the nonlinear time series, for which special models have been developed, for instance, autoregressive conditional heteroscedastic models.