  We study statistical properties of the $0^+$ spectrum of $^{208}$Pb in the
energy region $E_x\leq20$ MeV. We use the Skyrme interaction SLy4 as our model
Hamiltonian to create a single-particle spectrum and to analyze excited states.
The finite-rank separable approximation for the particle-hole interaction
enables us to perform the calculations in large configuration spaces. We show
that while the position of the monopole resonance centroid is determined by one
phonon excitations of $0^+$, the phonon-phonon coupling is crucial for the
description of a strength distribution of the $0^+$ spectrum. In fact, this
coupling has an impact on the spectral rigidity $\Delta_3(L)$ which is shifted
towards the random matrix limit of the Gaussian orthogonal ensembles.
