Abstract
This paper extends Whittle estimation to linear processes with a general stationary ergodic martingale difference noise. We show that such estimation is valid for standard parametric time series models with smooth bounded spectral densities, e.g., ARMA models. Furthermore, we clarify the impact of the hidden dependence in the noise on such estimation. We show that although the asymptotic normality of the Whittle estimates may still hold, the presence of dependence in the noise impacts the limit variance. Hence, the standard errors and confidence intervals valid under i.i.d. noise may not be applicable and thus require correction. The goal of this paper is to raise awareness to the impact of a non-i.i.d. noise in applied work.
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Acknowledgements
The authors would like to thank the two anonymous referees for valuable comments and suggestions. Liudas Giraitis and Murad S. Taqqu would like to thank Masanobu Taniguchi for his hospitality in Japan. M. Taniguchi was supported by JSPS Kiban grant A-15H02061 at Waseda University. The corresponding author states that there is no conflict of interest.
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Giraitis, L., Taniguchi, M. & Taqqu, M.S. Estimation pitfalls when the noise is not i.i.d.. Jpn J Stat Data Sci 1, 59–80 (2018). https://doi.org/10.1007/s42081-018-0004-8
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DOI: https://doi.org/10.1007/s42081-018-0004-8