Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

Abstract

a b s t r a c tIn this article we shall consider a class of strongly T -periodically correlated processes with values in a separable complex Hilbert space H.

Convergence Rate of Empirical Autocovariance Operators in H-Valued Periodically Correlated Processes

“…Besides, in 2011, Makagon introduced two transformations that map these sequences into T-dimensional stationary sequences and studied their properties. The spectral properties of such processes are studied by Makagon and Miamee (2013) and Soltani et al (2010) and Shishebor et al (2011) presented and examined the properties of their periodograms. Moreover, the class of PC autoregressive Hilbertian processes (PCARH) is considered by Soltani and Hashemi (2011) and the behavior of autocovariance and autocorrelation operators and their estimations are discussed in Haghbin et al (2017) and Hashemi et al (2019).…”

Periodically correlated autoregressive Hilbertian processes

“…These processes assume interesting time domain and spectral structures. The limiting behavior of the periodograms of PC Hilbertian processes of strong type are discussed in Soltani et al (2010) and Shishebor et al (2011), where a strong consistency and a central limit theorem are established. The PC Hilbertian processes in the context of Bosq Hilbertian processes have not yet been treated in detail.…”