Definition:White Noise Process

Definition

Let $S$ be a stochastic process consisting of a time series $\map {z_r} t$ such that:

the terms of the sequence $\sequence {z_r}$ are independent random variables

the terms of $\sequence {z_r}$ are governed by a normal distribution with zero expectation and a given variance $\sigma^2$.

Then $S$ is known as a white noise process.

Sources

• 1927: G. Udny Yule: On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers (Phil. Trans. Ser. A Vol. 226: pp. 267 – 298)  www.jstor.org/stable/91170

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

$1$: Introduction:

$1.2$ Stochastic and Deterministic Dynamic Mathematical Models

$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Linear filter model