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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 910828, 9 pages
Research Article

Outlier Detection in Adaptive Functional-Coefficient Autoregressive Models Based on Extreme Value Theory

1Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
2School of Finance and Statistics, East China Normal University, Shanghai 200241, China
3Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA

Received 26 January 2013; Accepted 12 March 2013

Academic Editor: Ming Li

Copyright © 2013 Ping Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes several test statistics to detect additive or innovative outliers in adaptive functional-coefficient autoregressive (AFAR) models based on extreme value theory and likelihood ratio tests. All the test statistics follow a tractable asymptotic Gumbel distribution. Also, we propose an asymptotic critical value on a fixed significance level and obtain an asymptotic -value for testing, which is used to detect outliers in time series. Simulation studies indicate that the extreme value method for detecting outliers in AFAR models is effective both for AO and IO, for a lone outlier and multiple outliers, and for separate outliers and outlier patches. Furthermore, it is shown that our procedure can reduce possible effects of masking and swamping.