Abstract
This chapter focuses on an alternative robust estimation/testing procedure for possibly infinite variance time series models. In the context of inference for heavy-tailed observation, least absolute deviations (LAD) estimators are known to be less sensitive to outliers than the classical least squares regression. This section generalizes the LAD regression-based inference procedure to the self-weighted version, which is a concept originally introduced by Ling (2005) for AR processes. Using the self-weighting method, we extend the generalized empirical likelihood (GEL) method to possibly infinite variance process, and construct feasible and robust estimation/testing procedures. The former half of this chapter provides a brief introduction to the LAD regression method for possibly infinite variance ARMA models, and construct the self-weighted GEL statistic following Akashi (2017). The desirable asymptotic properties of the proposed statistics will be elucidated. The latter half of this chapter illustrates an important application of the self-weighted GEL method to the change point problem of time series models.
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- 1.
Pan et al. (2007) proposed another self-weight of more general form \( \tilde{w}_{t-1} = ( 1 + \sum ^{t-1}_{k=1}k^{-\gamma }(\log k)^\delta |X(t-k)|)^{-\alpha }\) \((\gamma >2, \alpha \ge 2, \delta \ge 0)\). However, the optimal choice of the parameters in self-weights is highly nontrivial, so we confine ourselves to the self-weight of the form (5.6) to keep the focus of this section.
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© 2018 The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
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Liu, Y., Akashi, F., Taniguchi, M. (2018). Self-weighted GEL Methods for Infinite Variance Processes. In: Empirical Likelihood and Quantile Methods for Time Series. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-10-0152-9_5
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DOI: https://doi.org/10.1007/978-981-10-0152-9_5
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-10-0152-9
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