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Self-weighted least absolute deviation estimation for infinite variance autoregressive models

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Abstract:

Summary. 

How to undertake statistical inference for infinite variance autoregressive models has been a long-standing open problem. To solve this problem, we propose a self-weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded. Furthermore, a Wald test statistic is developed for the linear restriction on the parameters, and it is shown to have non-trivial local power. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given. The results are entirely different from other published results and should provide new insights for future research on heavy-tailed time series.

Keywords: Autoregressive model; Heavy-tailed time series; Infinite variance; Least absolute deviation estimation; Self-weighted least absolute deviation

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2005.00507.x

Affiliations: Hong Kong University of Science and Technology, People's Republic of China

Publication date: June 1, 2005

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