Single stock dynamics on high-frequency data: from a compressed coding perspective.

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.

Invariance in the recurrence of large returns and the validation of models of price dynamics.

Starting from a robust, nonparametric definition of large returns ("excursions"), we study the statistics of their occurrences, focusing on the recurrence process. The empirical waiting-time distribution between excursions is remarkably invariant to year, stock, and scale (return interval). This invariance is related to self-similarity of the marginal distributions of returns, but the excursion waiting-time distribution is a function of the entire return process and not just its univariate probabilities. Generalized autoregressive conditional heteroskedasticity (GARCH) models, market-time transformations based on volume or trades, and generalized (Lévy) random-walk models all fail to fit the statistical structure of excursions.

Testing and mapping non-stationarity in animal behavioral processes: a case study on an individual female bean weevil.

Statistical analysis based on two characteristics of a small-world network, and on Lempel-Ziv's measure of Kolmogorov-Chaitin's algorithmic complexity are first proposed to scan through an individual behavioral sequence for possible existence of non-stationarity. Due to fixed window width, these tests have drawbacks in mapping out regions of non-stationarity. A non-parametric approach based on sparse coding schemes is employed to segment the whole behavioral sequence into unequal length segments, thus resultant avoiding further efforts for grouping. Then attempts are made to entangle the resultant segmentation with other non-local behavioral patterns onto such sequence to ascertain that the non-stationarity corresponds to a sequence of different categories of underlying driving force. It is of potential importance that this segmentation, represented by a hierarchy of code sequences, provides a natural platform for detecting intrinsically coherent behavioral patterns based on continuously recorded data. Illustrations throughout the developments are made exclusively on data encoded from a nearly 4-h video-recording of a female bean weevil's behavior.