Definition:Deterministic Time Series
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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
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
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: