Alleviating Non-identifiability: a High-fidelity Calibration Objective for Financial Market Simulation with Multivariate Time Series Data

The non-identifiability issue has been frequently reported in the social simulation works, where different parameters of an agent-based simulation model yield indistinguishable simulated time series data under certain discrepancy metrics. This issue largely undermines the simulation fidelity yet lacks dedicated investigations. This paper theoretically analyzes that incorporating multiple time series data features in the model calibration phase can alleviate the non-identifiability exponentially with the increasing number of features. To implement this theoretical finding, a maximization-based aggregation function is applied to existing discrepancy metrics to form a new calibration objective function. For verification, the financial market simulation, a typical and complex social simulation task, is considered. Empirical studies on both synthetic and real market data witness the significant improvements in alleviating the non-identifiability with much higher simulation fidelity of the chosen agent-based simulation model. Importantly, as a model-agnostic method, it achieves the first successful simulation of the high-frequency market at seconds level. Hence, this work is expected to provide not only a rigorous understanding of non-identifiability in social simulation, but a high-fidelity calibration objective function for financial market simulations.