Rates of convergence of autocorrelation estimates for periodically correlated autoregressive Hilbertian processes. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Hashemi, Maryam; Zamani, Atefeh; Haghbin, Hossein
• Is Part Of: Statistics. Volume 53:Issue 2(2019)
• Page Start: 283
• Page End: 300
• Publication Date: 2019-03-04
• Subjects: Autocorrelation -- autoregressive processes -- estimation -- Hilbertian processes -- periodically correlated processes; 62G05 -- 62M10; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1547907
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Autoregressive Hilbertian (ARH) processes are of great importance in the analysis of functional time series data and estimation of the autocorrelation operators attracts the attention of various researchers. In this paper, we study estimators of the autocorrelation operators of periodically correlated autoregressive Hilbertian processes of order one (PCARH(1)), which is an extension of ARH(1) processes. The estimation method is based on the spectral decomposition of the covariance operator and considers two main cases: known and unknown eigenvectors. We show the consistency in the mean integrated quadratic sense of the estimators of the autocorrelation operators and present upper bounds for the corresponding rates.