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Stochastic process ε_{t} is White Noise if, for any moments of time s and t, the following holds:

1] E[ε_{t}] = 0,

2] E[ε_{t}^{2}] = σ^{2},

E[ε_{s} ε_{t}] = 0.

White noise can be defined in discrete or continuous time. Conditions 1] and 2] imply that white noise is a weakly stationary process. It is a very simple stationary process, in fact: the value today is uncorrelated with any values in the past or the future.

The spectral decomposition of white noise shows that different frequencies have the same amplitudes. The situation resembles that of white light. Hence the word “white” in the term “white noise”... The marginal distributions of white noise can be Gaussian or non-Gaussian, continuous or discrete (see this plot).

**WHITE NOISE REFERENCES
**

Greene, W. H. (2011). Econometric Analysis (7th ed). Upper Saddle River, NJ: Prentice Hall.

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

Brockwell, P. J., & Davis, R. A. (1991). Time Series: Theory and Methods (2nd ed). New York: Springer.

Wei, W. W. S. (1990). Time Series Analysis: Univariate and Multivariate Methods. Redwood City, CA: Addison Wesley.

Tsay, R. S. (2005). Analysis of Financial Time Series. New Jersey: Wiley-Interscience.

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