Definition:Statistical Time Series

Definition

A statistical time series is a time series whose future values can be described only in terms of a probability distribution.

Examples

Batch Process

Consider a manufacturing plant which outputs a product at some variable rate.

Let the output generate a discrete time series, obtained by accumulation.

It is not possible to know exactly what the output will be at a particular timestamp.

It is necessary instead to identify what particular probability distribution is obeyed by the data.

Also see

• Definition:Stochastic Model

• Definition:Deterministic Time Series

Sources

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

Part $\text {I}$: Stochastic Models and their Forecasting:

$2$: Autocorrelation Function and Spectrum of Stationary Processes:

$2.1$ Autocorrelation Properties of Stationary Models:

$2.1.1$ Time Series and Stochastic Processes: Deterministic and statistical time series