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Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results
Article first published online: 14 MAY 2004
DOI: 10.1111/j.1467-9892.2004.01775.x
Additional Information
How to Cite
Oppenheim, G. and Viano, M.-C. (2004), Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results. Journal of Time Series Analysis, 25: 335–350. doi: 10.1111/j.1467-9892.2004.01775.x
Publication History
- Issue published online: 14 MAY 2004
- Article first published online: 14 MAY 2004
- First Version received January 2001
- Abstract
- Article
- References
- Cited By
Keywords:
- Aggregation;
- Ornstein-Uhlenbeck;
- linear stochastic differential equations;
- random coefficients AR processes;
- seasonal long-memory
- 60E07;
- 60G10;
- 62M10;
- 60F17;
- 62M10
Abstract. It is shown that by aggregating simple random parameters, processes such as autoregressive micro-relationships or Ornstein-Uhlenbeck processes, one can obtain various seasonal long memory Gaussian models. The investigation concerns the discrete as well as the continuous time setting. In both situations the precise asymptotic behaviour of the covariance is studied. The regularity of sample paths is evaluated when possible.