Second-order robustness for time series inference

Xiaofei Xu (), Yan Liu () and Masanobu Taniguchi ()
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Xiaofei Xu: Wuhan University
Yan Liu: Waseda Univeristy
Masanobu Taniguchi: Waseda Univeristy

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 1, No 7, 213-225

Abstract: Abstract This paper studies the second-order asymptotics of maximum likelihood estimator (MLE) and Whittle estimator under $$\varepsilon $$ ε -contaminated model for Gaussian stationary processes. We evaluate the robustness of MLE and Whittle estimator based on the second-order Edgeworth expansion with an $$ \varepsilon $$ ε -disturbance spectral density. The measures of second-order robustness of MLE and Whittle estimator are investigated for concrete models with numerical study. The findings show that the MLE of Gaussian autoregressive process is robust in second-order term to a disturbance in spectral density under the middle level of spectral frequency, while it is more sensitive to a contamination under a too low frequency spectral mass. The Whittle estimator is robust to a moving average contamination when the Gaussian autoregressive process is not near unit root case, while it is sensitive to the disturbance under a nonregular situation in the case of near unit root.

Keywords: Gaussian stationary process; Spectral density; Second-order robustness; Edgeworth expansion; Whittle estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-023-09296-w

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