Abstract
This paper studies the second-order asymptotics of maximum likelihood estimator (MLE) and Whittle estimator under \(\varepsilon \)-contaminated model for Gaussian stationary processes. We evaluate the robustness of MLE and Whittle estimator based on the second-order Edgeworth expansion with an \( \varepsilon \)-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.
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Acknowledgements
Xu’s research was supported by a start-up research grant (No. 600460031) of Wuhan University. Liu was supported by JSPS Grant-in-Aid Scientific Research (C) 20K11719. Taniguchi’s research was supported by JSPS KAKENHI Kiban (S) Grand-in-Aid No. 18H05290.
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Xu, X., Liu, Y. & Taniguchi, M. Second-order robustness for time series inference. Stat Inference Stoch Process 27, 213–225 (2024). https://doi.org/10.1007/s11203-023-09296-w
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DOI: https://doi.org/10.1007/s11203-023-09296-w