Definition:Sample Mean of Stochastic Process
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Definition
Let $S$ be a stochastic process giving rise to a time series $T$.
The sample mean of $S$ over a set of $N$ successive values $\set {z_1, z_2, \dotsb, z_N}$ is defined as:
- $\overline z := \dfrac 1 N \ds \sum_{t \mathop = 1}^N z_t$
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: Mean and variance of a stationary process: $(2.1.3)$
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: