Definition:Weakly Stationary Stochastic Process
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Definition
Let $S$ be a stochastic process giving rise to a time series $T$.
$S$ is weakly stationary of order $f$ if and only if its moments up to some order $f$ depend only on time differences.
Such a condition is known as weak stationarity of order $f$.
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:
- $2.1.3$ Positive Definiteness and the Autocovariance Matrix: Weak stationarity
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: