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This paper presents a novel method to quantify seafarers' good seamanship during navigation scenarios with multi-vessel encounters -- in open and confined waters --, and to compute COLREG's-compliant trajectories for avoiding collision and grounding. The quantification of good seamanship requires knowledge about the state of the vessels (position, heading, and speed) and the surrounding sailing environment. Such information is accessible through the AIS system and the electronic nautical chart. The proposed method evaluates mutual collision risk by examining domain violations of each vessel, and comparing them to the seaman's actions. This results in a comprehensive metric of good seamanship. As risk free actions are not always possible in the resolution of a potential collision and grounding, the method adopts a branch-and-bound scheme to identify achievable maneuvers that minimize the risk. Further, the dynamic nature of vessel speed in congested scenarios is considered, recognizing potential changes in both own and target vessels' forward speeds. The proposed method is experimentally evaluated using historical AIS data and sea charts of Danish waters. This research contributes to the field by providing a more realistic perspective on seamanship in complex maritime environments., Comment: The 15th IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles (CAMS 2024)

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure.

The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to different assessment of situation at two approaching vessels. This may lead to high-risk conditions and could cause collision. This article considers decision making under uncertainty and suggests a novel method for probabilistic interpretation of vessel encounters that is explainable and provides a measure of uncertainty in the evaluation. The method is equally useful for decision support on a manned bridge as on Marine Autonomous Surface Ships (MASS) where it provides input for automated navigation. The method makes formal safety assessment and validation feasible. We obtain a resilient algorithm for machine interpretation of COLREGs under uncertainty and show its efficacy by simulations., Comment: Submitted to IEEE Transactions on Intelligent Transportation Systems

Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel subsampled quadrant estimator that improves efficiency while preserving consistency and robustness. This estimator is particularly well-suited for high-frequency financial data and we apply it to a large panel of US stocks. Our empirical analysis sheds new light on intra-day fluctuations in market betas by decomposing them into time-varying correlations and relative volatility changes. Our results show that intraday variation in betas is primarily driven by intraday variation in correlations.

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix. This can be avoided by a different parametrization, involving the logarithmic transformation of the block correlation matrix.