Statistics and Its Interface

Volume 4 (2011)

Number 2

A class of threshold autoregressive conditional heteroscedastic models

Pages: 149 – 157

DOI: http://dx.doi.org/10.4310/SII.2011.v4.n2.a10

Authors

Wai-Cheung Ip (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Yuan Li (School of Mathematics and Information Science, Guangzhou University, Guangzhou, China)

Heung Wong (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Xingfa Zhang (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Abstract

This paper generalizes Ling’s (2007) double AR($p$) model by considering a threshold effect in the mean equation. Provided the threshold is known, consistency and asymptotic normality of the quasi maximum likelihood estimators for the model are proved under weak conditions. Based on the Lagrange Multiplier principle, a threshold effect test is studied and its asymptotic null distribution is shown to be a functional of a zero-mean Gaussian process. Approximate methods are given to compute the upper percentage points and simulation results show that they perform well. From the empirical studies, we know that the original model can be improved when the threshold effect is considered.

Keywords

threshold AR(p) model, quasi maximum likelihood estimator, asymptotic normality, Lagrange multiplier test

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