Testing time reversibility without moment restrictions

In this paper we propose a class of new tests for time reversibility. It is shown that this test has an asymptotic normal distribution under the null hypothesis and non-trivial power under local alternatives. A novel feature of this test is that it does not have any moment restriction, in contrast with other time reversibility and linearity tests. Our simulations also confirm that the proposed test is very robust when data do not possess proper moments. An empirical study of stock market indices is also included to illustrate the usefulness of the new test.