This paper proposes a class of test procedures for a structural change with an unknown change point. In particular, we consider a general financial time series model with conditional heteroskedasticity. The test statistics are constructed via the empirical distribution approach and aim at detecting a change that may occur beyond the second moment. We derive the asymptotic null distributions of the test statistics and tabulate the critical values. Studies of the local power show that the test statistics have non-trivial local power. Finite sample performances of the proposed tests are studied via Monte Carlo methods. The test procedures are applied to test the change point in the S&P 500 daily index returns.