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Biometrika 2003 90(3):703-716; doi:10.1093/biomet/90.3.703
© 2003 by Biometrika Trust
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Testing and estimation of thresholds based on wavelets in heteroscedastic threshold autoregressive models

Wai-Cheung Ip1, Heung Wong1, Yuan Li2 and Hongzhi An3

1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kongmathipwc{at}polyu.edu.hk mathwong{at}polyu.edu.hk 2 Department of Mathematics, Guangzhou University, Guangzhou 510405, China.yli57{at}hotmail.com 3 Institute of Applied Mathematics, The Chinese Academy of Sciences, Beijing 100080, China. ahz{at}mail.amt.ac.cn

We consider the testing and estimation of thresholds in heteroscedastic threshold autoregressive models with an unknown number of thresholds. A test statistic based on empirical wavelet coefficients is proposed.The asymptotic distribution of the test statistic is established and consistent estimators of the thresholds and the number of thresholds are given. A Monte Carlo study and a real example are used to assess the performance of our method.

Key Words: Heteroscedasticity; Jump point; Threshold; Time delay; Wavelet

Received September 2001. Revised October 2002


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