Positivity of a MA(2) or MA(3) covariance

Positivity of a MA(2) or MA(3) covariance

Bernard Picinbono 

Laboratoire des signaux et systèmes (L2S, UMR CNRS 8506), université Paris-Sud CNRS – Centrale-Supelec, 3, rue Joliot-Curie, 91192 Gif-sur-Yvette, France

31 December 2016
| Citation

The covariance function gk of a real discrete-time moving average of order q random signal is zero for k ≥ q but its other values must satisfy some conditions ensuring that gk 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 c of components gk belongs to this domain then gk 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.


MA and AR signals, conditions of the covariance, covariance matrices.

1. Introduction
2. Fonction de covariance d’un signal MA(2)
3. Fonction de covariance d’un signal MA(3)
4. Conclusion

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