Definition:Discrete Time Series/Accumulation

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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.



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


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: $2$