In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to describe the steps and properties of HS. We then use empirical data on daily affect from one couple to illustrate the use of HS for describing the affective dynamics of the dyad. First, we partition the data into three periods that represent different affective states and show different dynamics between both individuals’ affect. We then examine the synchrony between both individuals’ affective states and identify different patterns of coherence across the periods. Finally, we discuss the possibilities of using results from HS to construct confirmatory dynamic models with multiple change points or regime-specific dynamics.

We address the question: How do we non-parametrically decode the unknown state-space vector underlying a lengthy discrete time series? The time series of concern is governed by one non-autonomous dynamics with only two internal states. This question pertinently reflects the dilemma of computing infeasibility against inferential bias found in many scientific areas. This dilemma becomes an issue when considering whether to have, or not to have likely very unrealistic structural assumptions on the state-space dynamics in most of real-world applications. To resolve this dilemma, the decoding problem is transformed into an event-intensity change-point problem without prior knowledge of the number of change-points involved. A new decoding algorithm, called Hierarchical Factor Segmentation (HFS), is proposed to achieve computability and robustness. Performance of the HFS algorithm in terms of total decoding error is compared to the decoding benchmark Viterbi algorithm through computer experiments. Under Hidden Markov Model (HMM) settings with true parameter values, our HFS algorithm is competitive against the Viterbi algorithm. Interestingly, when the Viterbi algorithm operates with maximum likelihood estimated (MLE) parameter values, our HFS algorithm performs significantly better. Similar favorable results are found when the Markov assumption is violated. We further demonstrate one very important application of our HFS algorithm in bioinformatics as a promising computational solution for finding CpG islands—DNA segments with aggregated CpG dinucleotides—on a genome sequence. A real illustration on a subsequence of human chromosome #22 is carried out and compared with one popular search algorithm.

High-frequency return, trading volume and transaction number are digitally coded via a nonparametric computing algorithm, called hierarchical factor segmentation (HFS), and then are coupled together to reveal a single stock dynamics without global state-space structural assumptions. The base-8 digital coding sequence, which is capable of revealing contrasting aggregation against sparsity of extreme events, is further compressed into a shortened sequence of state transitions. This compressed digital code sequence vividly demonstrates that the aggregation of large absolute returns is the primary driving force for stimulating both the aggregations of large trading volumes and transaction numbers. The state of system-wise synchrony is manifested with very frequent recurrence in the stock dynamics. And this data-driven dynamic mechanism is seen to correspondingly vary as the global market transiting in and out of contraction-expansion cycles. These results not only elaborate the stock dynamics of interest to a fuller extent, but also contradict some classical theories in finance. Overall this version of stock dynamics is potentially more coherent and realistic, especially when the current financial market is increasingly powered by high-frequency trading via computer algorithms, rather than by individual investors.