# discrete white noise

The stochastic process^{} $\{{Z}_{t},t\in T\}$,where T is the set of natural integers $\mathbb{N}$ or the set of all integers $\mathbb{Z}$, is said to be white noise with mean 0 and variance ${\sigma}^{2}$, written
$\{{Z}_{t}\}\sim WN(0,{\sigma}^{2})$, if and only if $\{{Z}_{t}\}$ has zero mean and autocovariance function

$$\gamma \left(h\right)=\{\begin{array}{cc}{\sigma}^{2}\hfill & \text{if}h=0\hfill \\ 0\hfill & \text{if}h\ne 0\hfill \end{array}$$ |

Title | discrete white noise |
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Canonical name | DiscreteWhiteNoise |

Date of creation | 2013-03-22 15:20:24 |

Last modified on | 2013-03-22 15:20:24 |

Owner | georgiosl (7242) |

Last modified by | georgiosl (7242) |

Numerical id | 8 |

Author | georgiosl (7242) |

Entry type | Definition |

Classification | msc 60G10 |

Classification | msc 60H40 |