A portmanteau test for the iid hypothesis

Abstract

In this paper, we introduce a new portmanteau test for the iid hypothesis, where the elements of the sample are allowed to take values in a general space (e.g., a function space). We study the finite sample properties of our test, evaluating its performance in terms of empirical size and power. In particular, we compare the empirical power of our test with the power of other tests in the literature designed to work in a specific data setting, as the one‐way analysis of variance test used in experimental data analysis and three portmanteau tests used in time series analysis. In every case, we found conditions where our test outperformed in power to the competing test. Finally, to illustrate the usefulness of our test, we implement it on two real‐world applications based on function‐valued data.