Continuous-Time Stochastic Processes with Cyclical Long-Range Dependence
Article first published online: 2 JUN 2004
Australian & New Zealand Journal of Statistics
Volume 46, Issue 2, pages 275–296, June 2004
How to Cite
Anh, V.V., Knopova, V.P. and Leonenko, N.N. (2004), Continuous-Time Stochastic Processes with Cyclical Long-Range Dependence. Australian & New Zealand Journal of Statistics, 46: 275–296. doi: 10.1111/j.1467-842X.2004.00329.x
- Issue published online: 2 JUN 2004
- Article first published online: 2 JUN 2004
- Received April 2002; revised October 2002; accepted November 2002.
- Cited By
- Gegenbauer process;
- long-range dependence;
- stationary processes
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.