Since recent history has shown that financial crises erupting in one market are likely to spill over to other markets, the analysis of financial contagion attained greater attention. Moreover, there is a common notion among researchers that dependence between financial time series is subject to structural changes. In this paper, financial contagion is modelled by means of hierarchical Archimedean copulas (HAC) for the US, the German and the Japanese stock market. The time-varying nature of the copula parameters is induced by adopting the local parametric approach introduced in Spokoiny (1998) and applied in Härdle et al. (2010). In the latter research paper, the critical values for the sequential testing procedure underlying this approach are simulated on the basis of some predefined copula parameter constellations. However, it is known that the underlying parameter constellations drive the critical values. The contribution of this paper is the adaptive simulation of the critical values according to the true parameter constellations. In this way, this paper aims at refining the estimation method conducted in Härdle et al. (2010). It can be seen that the estimation results differ substantially as one simulates the critical values by means of the true parameter constellations.