Definition:Discrete Time Series/Accumulation

Definition

A discrete time series can be obtained by collecting a varying quantity over a period of time.

The observations are the measurements of the quantities at the end of each period.

Examples

Rainfall

An example of a discrete time series obtained by accumulation of a quantity would be the contents of a collector of rainfall.

At the end of each time period, usually a day, the rainfall is collected from the container and its volume is measured.

The container is emptied again, ready for the rainfall to be collected over the next period.

Batch Process

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

The output can yield a discrete time series, obtained by accumulation of this output over a specified time period.

Also see

• Definition:Discrete Time Series by Sampling

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: Time series: $2$