Roy, A., Dattner, I., Podder, M. Adaptive rate-optimal lack-of-fit testing for systems of ordinary differential equations. [Working paper]
Abstract: We introduce an omnibus lack-of-fit test for nonlinear ODE models using a minimax nonparametric framework. Our approach applies to both single-state and multi-state ODEs, including cases with unobserved states, making it a versatile tool for model assessment. The proposed test is adaptive and rate-optimal, adjusting to the unknown smoothness of alternatives while maintaining uniform consistency. We establish its theoretical validity through a minimax analysis and demonstrate its effectiveness via simulations and real-world applications in biology, agriculture, and drug research.
Roy, A., Mukherjee, S., Deb, S. Nonparametric estimation of shape-constrained time series regression model.
Abstract: In a nonparametric regression model we assume the regression function to satisfy some pre-specified theoretical constraints like monotonicity, convexity or quasiconvexity, which are common in financial and economic models. We introduce a novel approach using shape-enforcing operators, with proven asymptotic behavior and efficient algorithms. Simulations show improved model performance, offering more interpretable and reliable outcomes.
Roy, A., Narang, A., Guha, A., Chakrabarti, A.S. De-factoring financial returns: Changes in the topological characteristics of networks. [Working paper ]
Abstract: Financial markets evolve through complex interactions among trading agents, making it challenging to retain full system information. To simplify networks, we apply filtering techniques that extract core linkages between nodes. We construct networks using correlation (short-term), Granger causality, and cointegration (long-term) relationships, refining them by removing aggregate trends that mask idiosyncratic movements. Our results show that combining network topologies with filtering enhances the understanding of co-movements and causal dynamics in financial systems.