# Definition:Discrete Time Series/Accumulation

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## 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

## 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: $2$

- $2.1$ Autocorrelation Properties of Stationary Models:

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

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