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Continuous-Time Stochastic Processes with Cyclical Long-Range Dependance

By Vo V. Anh, Viktoriya P. Knopova and Nikolai N. Leonenko


We introduce continuous-time random processes whose spectral density is unbounded at some non-zero frequencies. The discretized versions of these processes have asymptotic properties similar to those of discrete-time Gegenbauer processes. We present some properties of the covariance function and spectral density as well as a theory of statistical estimation of the mean and covariance function of such processes. Some direction for further generalizations of the results are indicated

Topics: 010406 Stochastic Analysis and Modelling, continuous, time processes, simgular spectrum, long, range dependance, Gegenbauer process
Publisher: Blackwell Publishing
Year: 2004
DOI identifier: 10.1111/j.1467-842X.2004.00329.x
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