# 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.

## Sources

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: $2$