UCL Discovery

Abstract

In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (X-n) with several regimes. We suppose that the underlying process (I-n) which drives the evolution of (X-n) is stationary. Under some dependence assumptions on (I-n), we prove the existence of a unique stationary solution, and with a symmetric compact autocorrelation operator, we can state a law of large numbers with rates and the consistency of the covariance estimator. An overall hypothesis states that the regimes where the autocorrelation operator's norm is greater than 1 should be rarely visited.