Testing for a Change in Correlation at an Unknown Point in Time Using an Extended Functional Delta Method

Abstract

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to recent stock returns.

Monitoring correlation change in a sequence of random variables

“…whereD is an estimator which is calculated from the first m observations and is given in the appendix, see also Wied et al (2011). We stop and declare H 0 to be invalid at the first time k such that the detector V k exceeds the value of a scaled threshold function w, therefore yielding the stopping rule:…”

“…Once the presence of a correlation change is detected, an estimate of its location is provided by using the statistic proposed in Wied et al (2011). The estimate of the change point is k = arg max…”

Dating multiple change points in the correlation matrix

“…This approach allows the practitioner to determinate if there is a change or not but he cannot determine where a possible change occurs or how many changes there are. Wied et al (2012) fill this gap by proposing an algorithm based on the correlation constancy test to estimate both the number and the timing of possible change points. However, the previous papers only consider bivariate correlations that restricts the applicability of these procedures when more than two variables are of interest.…”

“…For instance, in portfolio management, typically the interest is in more than two assets and constancy of the whole correlation matrix is of interest. Recently, Wied (2014) has proposed a CUSUM statistic that extends the methodology from the test proposed by Wied et al (2012) to higher dimensions, but keeping its nonparametric and model-free approach. Wied (2014) show that the matrix-based test outperforms a method based on performing several pairwise tests and to use a level correction like Bonferroni-Holm in some situations.…”

Change Point Analysis of Correlation in Non-stationary Time Series

“…For example, Inclán and Tiao (1994) and Aue et al (2009) assume for the construction of a testing procedure for the hypothesis for change point in the variance that the mean of the sequence under consideration does not change in time (as the variance under the null hypothesis). A similar assumption was made by Wied et al (2012) in the context of testing for a constant correlation, where the authors suggested a CUSUM-type statistic for a change in the correlation of a stationary time series if at the same time the means and variances do not change. However, from a practical point of view, assumptions of this type are very restrictive and there might be many situations where one is interested in a change of the correlation even if the mean and the variances change gradually in time.…”