Purpose This study aims to investigate the dynamic co-movement and interconnection among 69 security investment indices in China using the multi-time scale framework. Design/methodology/approach The authors first use the multiple coherence analysis method to exhibit the degree of relationships among the variables under study. In addition, the wavelet multiple correlation and wavelet multiple cross-correlation analyses are used to examine the time-frequency synchronization interdependence structure among the variables. Findings From the empirical findings, one may infer less opportunity for portfolio diversification at higher time scales. Obviously, at these scales, the authors find that the 69 Chinese investment indices generate a simple security investment class, as indicated by higher interconnection between the indices. Research limitations/implications Further research can increase the sample size to re-investigate the empirical relationship for security investment indices. Practical implications In the nutshell, the results demonstrate the potential for Chinese investors to invest in security investment indices to earn from portfolio diversification at lower time frequencies. The Chinese investment market indices under study yield further opportunities of portfolio diversification toward the short-term investors than the long-term investors. Originality/value To the best of the authors’ knowledge, this is the first paper to examine the dynamic co-movement and interconnection for security investment indices in China.