New Combined Permutation Test With Application to Time Series Comparison for the Assessment of ESG Investment Financial Performance

ABSTRACT The nonparametric family of combined permutation tests is composed of a large number of members, each one characterized by a specific combining function. Each combined permutation test has a different power behavior, depending on the characteristics and complexity of the problem. The comparison of groups of dependent and high‐dimensional time series represents a challenging inferential problem for which classical parametric methods often rely on restrictive assumptions. To address this aspect, we propose a new combined permutation test and, through a simulation study, we investigate its performance and detect the conditions under which it is preferable to the most commonly used combined permutation tests. Furthermore, a general formula for the nonparametric combination, called generalized combining function, is proposed to better understand how the new test fits into the broader family of combined permutation tests. The combined test statistics are analyzed from a new perspective. Finally, the new test is proposed as a solution to the problem of comparing groups of time series. A contribution to the empirical literature about the financial performance of ESG titles is provided by applying such a solution to real financial data.