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  1. Volatility modeling is crucial in finance, especially when dealing with intraday transaction‐level asset returns. The irregular and high‐frequency nature of the data presents unique challenges. While stochastic volatility (SV) models are widely used for understanding patterns in volatility of daily stock returns which constitute regularly spaced time series, new classes of models must be introduced for analyzing volatility in irregularly spaced intraday data. Specifically these models must accommodate the random gaps between successive transactional events. By modeling the gaps using autoregressive conditional duration (ACD) models, we describe a hierarchical irregular SV autoregressive conditional duration (IR‐SV‐ACD) model for estimating and forecasting intertransaction gaps and the volatility of log‐returns. We carry out the analysis in the Bayesian framework via the Hamiltonian Monte Carlo (HMC) algorithm with No‐U‐turn sampler (NUTS) in R using thecmdstanrpackage. The fits and forecasts are obtained using Monte Carlo averages based on the posterior samples. We illustrate this approach using simulation studies and real data analysis for intraday prices available at microseconds level of health stocks traded on the New York Stock Exchange (NYSE). The log‐returns and gaps are calculated for the stocks and are used for modeling.

     
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  2. Free, publicly-accessible full text available August 1, 2024
  3. Abstract Background

    Immune responses need to be initiated rapidly, and maintained as needed, to prevent establishment and growth of infections. At the same time, resources need to be balanced with other physiological processes. On the level of transcription, studies have shown that this balancing act is reflected in tight control of the initiation kinetics and shutdown dynamics of specific immune genes.

    Results

    To investigate genome-wide expression dynamics and trade-offs after infection at a high temporal resolution, we performed an RNA-seq time course onD. melanogasterwith 20 time points post Imd stimulation. A combination of methods, including spline fitting, cluster analysis, and Granger causality inference, allowed detailed dissection of expression profiles, lead-lag interactions, and functional annotation of genes through guilt-by-association. We identified Imd-responsive genes and co-expressed, less well characterized genes, with an immediate-early response and sustained up-regulation up to 5 days after stimulation. In contrast, stress response and Toll-responsive genes, among which were Bomanins, demonstrated early and transient responses. We further observed a strong trade-off with metabolic genes, which strikingly recovered to pre-infection levels before the immune response was fully resolved.

    Conclusions

    This high-dimensional dataset enabled the comprehensive study of immune response dynamics through the parallel application of multiple temporal data analysis methods. The well annotated data set should also serve as a useful resource for further investigation of theD. melanogasterinnate immune response, and for the development of methods for analysis of a post-stress transcriptional response time-series at whole-genome scale.

     
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