A bootstrap bias correction of long run fourth order moment estimation in the CUSUM of squares test

ABSTRACT

The aim of this paper is to propose a bias correction of the estimation of the long run fourth order moment in the CUSUM of squares test proposed in Sansó et al. [Testing for change in the unconditional variance of financial time series. Rev Econ Financ. 2004;4(1):32–53] for the detection of structural breaks in financial data. The correction is made by using the stationary bootstrap. The choice of this resampling technique is justified by the stationarity and weak dependence of the time series under the assumptions which ensure the existence of the limiting distribution of the test statistic, under the null hypothesis. Monte Carlo experiments have been implemented to evaluate the effect of the proposed bias correction considering two particular data generating processes, the GARCH(1,1) and the log-Normal Stochastic Volatility. The effectiveness of the bias correction has been evaluated also on real data sets.

KEYWORDS:

• Bias correction
• CUSUM of squares test
• structural breaks

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62P20
• 62F40

Acknowledgments

The author gratefully thanks the anonymous referees for their useful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Davide De Gaetano  http://orcid.org/0000-0001-9617-781X