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Keywords:

  • Gegenbauer process;
  • long-range dependence;
  • stationary processes

Summary

This paper introduces 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. The paper presents 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 directions for further generalizations of the results are indicated.