Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes

M. D. Ruiz-Medina () and R. M. Espejo ()
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M. D. Ruiz-Medina: Faculty of Sciences, University of Granada
R. M. Espejo: University of Granada

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 207-222

Abstract: Abstract The autoregressive Hilbertian process framework has been introduced in Bosq (2000). This book provides the nonparametric estimation of the autocorrelation and covariance operators of the autoregressive Hilbertian processes. The asymptotic properties of these estimators are also provided. The maximum likelihood approach still remains unexplored. This paper obtains the asymptotic distribution of the maximum likelihood (ML) estimators of the auto-covariance operator of the Hilbert-valued innovation process, and of the autocorrelation operator of a Gaussian autoregressive Hilbertian process of order one. A real data example is analyzed in the financial context for illustration of the performance of the projection maximum likelihood estimation methodology in the context of missing data.

Keywords: Autoregressive Hilbertian processes; Central limit results; EM algorithm; Financial data; Maximum likelihood estimation; Missing functional data; Numerical projection methods; 60G42; 60G15; 62E20; 62F12 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9329-8

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