Analysis framework for higher-order temporal correlations with applications to human heartbeats

We propose a time series analysis framework focused on higher-order temporal correlations in the event sequence beyond the interevent time distribution by employing the burst-tree decomposition method. Bursts are clustered events that rapidly occur within shorter time periods, and they are separated by relatively longer inactive periods. The burst-tree decomposition method exactly maps the event sequence onto a tree, called a burst tree, in which each internal node represents a merge of consecutive bursts at the timescale separating those bursts. The burst tree fully reveals the hierarchical structure of bursts, hence the higher-order temporal correlations for the entire range of timescales. Those correlations are quantified using novel and existing measures derived from the burst tree, such as the burst complexity, memory coefficient for bursts, and principal and secondary cross sections of the burst-merging kernel. We apply our framework to the heartbeat time series of healthy people and of those with heart disease to reveal distinct multiscale temporal properties in physiological time series.