On the regularity of spectral densities of continuous-time completely linearly regular processes

Alejandro Murua

Stochastic Processes and their Applications, 1999, vol. 79, issue 2, 213-227

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([tau]-(r+[mu])) as [tau] --> +[infinity], for some , [mu] [set membership, variant] (0,1], then the spectral density has at least r uniformly continuous, bounded, and integrable derivatives, with the rth derivative satisfying a Lipschitz continuity condition of order [mu]. 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.

Keywords: Weakly; stationary; stochastic; process; Continuous-time; process; Complete; linear; regularity; Spectral; density; Strong; mixing (search for similar items in EconPapers)
Date: 1999
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