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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2015; 52(3): 503-522

Printed May 1, 2015

https://doi.org/10.4134/JKMS.2015.52.3.503

Copyright © The Korean Mathematical Society.

Parameter change test for nonlinear time series models with GARCH type errors

Jiyeon Lee and Sangyeol Lee

Seoul National University, Seoul National University

Abstract

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In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

Keywords: nonlinear time series models with GARCH type errors, parameter change, CUSUM test, weak convergence to a Brownian bridge

MSC numbers: 62M10

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