A parametric bootstrap test for cycles

The paper proposes a simple test for the hypothesis of strong cycles and as a by-product a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi) Gaussian process G(τ), τ∈[0,1]. Because the covariance structure of G(τ) is a complicated function of τ and model dependent, to obtain the critical values (if possible) of maxτ∈[0,1]G(τ) may be difficult. For this reason, we propose a bootstrap scheme in the frequency domain to circumvent the problem of obtaining (asymptotically) valid critical values. The proposed bootstrap can be regarded as an alternative procedure to existing bootstrap methods in the time domain such as the residual-based bootstrap. Finally, we illustrate the performance of the bootstrap test by a small Monte-Carlo experiment and an empirical example.