Nowadays, quantification of complex time series, in terms of multifractality, finds a multitude of applications in diverse areas. However, thus far the majority of the related studies presented in the scientific literature often focus on analysis of singularity spectrum width as a signature of the hierarchical organization and measure of the complexity degree. The time series generated by intricate processes may include many convoluted components with different hierarchy. Even more, contribution of such components in aggregated signal vary in time and results in its sophisticated dynamics. This concept can be almost directly applied to the stock market indices as they are built of components that have different characteristics. Furthermore, financial markets are constantly exposed to the external factors which may reduce or increase the influence of particular company shares on the index. In present contribution we analysed daily data from two major stock market indices (S&P500 and NASDAQ) and it was shown that they reveal multiscaling features. Moreover, hierarchical organization of the financial time series evolves in time which is often correlated with historically significant events and market crashes. Distortion of the temporal organization of the data is clearly visible on the level of multifractal spectra which are characterized by strongly asymmetric shape after 1985 in contrast to almost symmetric one for the earlier period (Figure 1). We believe that our findings can be potentially useful in financial engineering and serve market regulators as a additional indicator of market state.