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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.
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