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

Paper: arXiv 2407.16566

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper contains significant theoretical derivations and proofs regarding non-identifiability and aggregation functions, indicating high mathematical density. However, the empirical validation, while mentioned on synthetic and real data, appears more methodological and lacks detailed implementation code, backtest results, or statistical metrics typical of fully deployment-ready work.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Alleviate non-identifiability in<br>Financial Market Simulation calibration"] --> B["Input: Multivariate Time Series Data"]
  B --> C["Key Methodology<br>High-fidelity Calibration Objective<br>Maximization-based aggregation of multiple discrepancy metrics"]
  C --> D{"Computation<br>Calibrate FMS Model using<br>Proposed Objective Function"}
  D --> E["Key Outcomes"]
  
  E --> F["Theoretical Proof: Exponential reduction in non-identifiability<br>as feature count increases"]
  E --> G["Empirical Results: Higher simulation fidelity<br>on synthetic & real market data"]
  E --> H["Robustness: Effective with non-linearly<br>correlated features"]

Cited References (71)

1. QuantFactor REINFORCE: Mining Steady Formulaic Alpha Factors with Variance-bounded REINFORCE — → 2409.05144
2. Rhine: A regime-switching model with nonlinear representation for discovering and forecasting regimes in financial markets (2024)
3. KAN4Drift: Are KAN Effective for Identifying and Tracking Concept Drift in Time Series? (2024)
4. A survey of explainable artificial intelligence (XAI) in financial time series forecasting (2024) — link
5. Kolmogorov-arnold networks for time series: Bridging predictive power and interpretability (2024) — link
6. Predict stock prices using supervised learning algorithms and particle swarm optimization algorithm (2023)
7. Hybrid of jellyfish and particle swarm optimization algorithm-based support vector machine for stock market trend prediction (2024)
8. A deep learning integrated framework for predicting stock index price and fluctuation via singular spectrum analysis and particle swarm optimization (2024)

1 of 71 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.