Abstract
This paper deals with the study of the relationship between the complete linear regularity of continuous-time weakly stationary processes and the smoothness of their spectral densities. It is shown that when the coefficient of complete linear regularity behaves like O( τ −( r + μ ) ) as τ → +∞ , for some r ∈ N , μ ∈ (0,1] , then the spectral density has at least r uniformly continuous, bounded, and integrable derivatives, with the r th derivative satisfying a Lipschitz continuity condition of order μ . Conversely, under certain smoothness assumptions on the spectral density, upper bounds on the rate of decay of the coefficient of complete linear regularity are obtained.
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