Multivariate Data

Sig-Splines: universal approximation and convex calibration of time series generative models ArXiv ID: 2307.09767 “View on arXiv” Authors: Unknown Abstract We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a seamless substitution for traditional neural networks. This approach enables us to achieve not only the universality property inherent in neural networks but also introduces convexity in the model’s parameters. ...

Non-parametric cumulants approach for outlier detection of multivariate financial data ArXiv ID: 2305.10911 “View on arXiv” Authors: Unknown Abstract In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit n-circle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises. ...