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.

Also see

• Definition:Deterministic Model

• Definition:Statistical Time Series

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: Deterministic and statistical time series