# Definition:Deterministic Time Series

## Definition

A deterministic time series is a time series whose future values can be determined exactly by calculation of a mathematical function.

## Examples

### Arbitrary Cosine Function

Consider the time series $T$ whose future values are determined by the function:

$z_t = \map \cos {2 \pi f t}$

for some constant $f$.

Then $T$ is a deterministic time series.

## 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: Deterministic and statistical time series