Definition:Statistical Time Series

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


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


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