An adjusted-range based self-normalization test for correlation change

Abstract

This paper proposes an adjusted-range based self-normalized test for change in correlation. Unlike the self-normalization approach proposed by Lobato (2001) and Shao (2010), which relies on the variance of the partial sum process as a self-normalizer, and used by Choi and Shin (2020) to formulate the self-normalized Q test statistic, here we propose the use of an adjusted-range of the partial sum process instead. Similar to the self-normalized Q test statistic in Choi and Shin (2020), our adjusted-range based correlation change test is also nuisance parameter and distribution free, which helps to circumvent the kernel-based long-run variance (LRV) estimation in Wied et al. (2012) and the computationally expensive bootstrapping in Wied (2017). Moreover, the proposed adjusted-range based correlation change test is a portmanteau test with a neater formulation than Q; it is found to have adequate sizes and powers in many cases and it has much better powers than Q under serial dependence with either homoscedasticity or heteroscedasticity. The empirical analysis also suggests the adequacy of the proposed test.