Periodically Correlated Space-Time Autoregressive Hilbertian Processes

Abstract

In this paper, we introduce periodically correlated space-time autoregressive processes with values in Hilbert spaces. The existence conditions and the strong law of large numbers are established. Moreover, we present an estimator for the autocorrelation parameter of such processes.

Keywords

• Hilbertian processes
• Periodically correlated space-time autoregressive processes
• Strong law of large numbers
• T-periodic sequences