Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results

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.