Positivité d'une covariance de type MA(2) ou MA(3)

Abstract : The covariance function $\gamma _k$ of a real discrete-time moving average of order $q$ random signal is zero for $k > \vert q \vert$ but its other values must satisfy some conditions ensuring that $\gamma _k$ is a non-negative-definite function, which means that its Fourier transform, or its power spectrum, is non-negative. There are some general conditions ensuring this property but they cannot be used in order to determine the domain $D_+$ such that when the vector ${\bf c}$ of components $\gamma _k$ belongs to this domain then $\gamma _k$ has the required non-negative property. The boundaries of the domain are determined for $q = 2$ and $q = 3$ theoretically and computer simulations exhibit an excellent agreement between theoretical and simulated results.
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Bernard Picinbono. Positivité d'une covariance de type MA(2) ou MA(3). Traitement du Signal, Lavoisier, 2016, 22 (4), pp. 403-414. ⟨hal-01656610⟩

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