Fourier-type tests of mutual independence between functional time series

Abstract

We suggest tests of independence between time series of functional observations. The tests are based on characteristic functions which are appropriately estimated from functional observations. The limit distribution of the new test statistic is obtained under the null hypothesis, while under alternatives it is shown that the same test statistic almost surely diverges as the sample size increases. Since the limit null distribution is complicated, a bootstrap version of the test is suggested to assess the test’s performance in finite samples. Also, an application illustrates the use of the method with real data from financial markets. Extension to tests of mutual independence for multiple time series is also considered.