Spectral analysis of long range dependence functional time series

2019/12/15 by M. D. Ruiz‐Medina, Ruiz-Medina, M. Dolores · 2 citations
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Complex Systems and Time Series Analysis #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1912.07086

Abstract

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario, a weak--consistent parametric estimator of the long--memory operator is then obtained by minimizing, in the norm of bounded linear operators, a divergence information functional loss.

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• An LRD spectral test for irregularly discretely observed contaminated functional time series in manifolds
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