Strictly Stationary Stochastic Process/Examples/Autocovariance
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Example of Strictly Stationary Stochastic Process
Let $S$ be a strictly stationary stochastic process giving rise to a time series $T$.
It is necessary that:
- The autocovariance between every two observations $z_t, z_{t + k}$ separated by a given lag $k$
is the same as:
- the autocovariance between every other two observations $z_{t + m}, z_{t + m + k}$separated by a given lag $k$
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:
- $2.1.2$ Stationary Stochastic Processes: Autocovariance and autocorrelation coefficients
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: