A time series is a sequence of observations indexed in time order. A finite observed series can be written as ,
or it can be modeled as one realization of a stochastic
process
.
The time index may be discrete or continuous, and each observation may be a scalar
or vector.
Temporal ordering distinguishes a time series from an unordered sample and permits dependence between observations at different times. The study of this dependence and its use in modeling and forecasting is called time series analysis.