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

TL;DR

This paper introduces a new calibration objective that uses multiple time series features to significantly reduce non-identifiability in social simulations, improving fidelity in financial market models.

Contribution

It provides a theoretical and empirical framework for using multiple features to alleviate non-identifiability, along with a practical aggregation function for calibration.

Findings

Significant reduction in non-identifiability with multiple features

Enhanced simulation fidelity on synthetic and real data

Robustness to feature selection as long as features are uncorrelated

Abstract

The non-identifiability issue has been frequently reported in 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 demonstrates that incorporating multiple time series data features during the model calibration phase can exponentially alleviate non-identifiability as the number of features increases. To implement this theoretical finding, a maximization-based aggregation function is proposed based on existing discrepancy metrics to form a new calibration objective function. For verification, the task of calibrating the Financial Market Simulation (FMS), a typical yet complex social simulation, is considered. Empirical studies confirm the significant improvements in alleviating the non-identifiability of calibration tasks. Furthermore, as a model-agnostic method, it achieves much higher simulation fidelity of the chosen FMS model on both synthetic and real market data. Moreover, it is both theoretically and empirically analyzed that as long as the features are selected and not linearly correlated, they can contribute to alleviation, which demonstrates the robustness of the proposed objective. Hence, this work is expected to provide not only a rigorous understanding of non-identifiability in social simulation but also an off-the-shelf high-fidelity calibration objective function for FMS.