Bootstrap procedures for variance breaks test in time series with a changing trend

ABSTRACT

In this article, we consider the problem of testing for variance breaks in time series in the presence of a changing trend. In performing the test, we employ the cumulative sum of squares (CUSSQ) test introduced by Inclán and Tiao (1994, J. Amer. Statist. Assoc., 89, 913 − 923). It is shown that CUSSQ test is not robust in the case of broken trend and its asymptotic distribution does not convergence to the sup of a standard Brownian bridge. As a remedy, a bootstrap approximation method is designed to alleviate the size distortions of test statistic while preserving its high power. Via a bootstrap functional central limit theorem, the consistency of these bootstrap procedures is established under general assumptions. Simulation results are provided for illustration and an empirical example of application to a set of high frequency real data is given.

KEYWORDS:

• Bootstrap
• Changing trends
• CUSSQ test
• Variance breaks.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05
• 62F03

Additional information

Funding

Supported in part by a National Natural Science Foundation of China Grant No. 71473194, No. 71273206, and No. 71103143; Shaanxi Natural Science Foundation of China Grant No. 2013KJXX-40, 2017JM1042, and 2016KJ1500.