Forward-Oriented Causal Observables for Non-Stationary Financial Markets

ArXiv ID: 2512.24621 “View on arXiv”

Authors: Lucas A. Souza

Abstract

We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available up to the decision time. Rather than proposing a machine-learning predictor or a direct price-forecast model, we focus on \emph{“constructing”} an interpretable causal signal from heterogeneous micro-features that encode complementary aspects of the dynamics (momentum, volume pressure, trend acceleration, and volatility-normalized price location). The construction combines (i) causal centering, (ii) linear aggregation into a composite observable, (iii) causal stabilization via a one-dimensional Kalman filter, and (iv) an adaptive ``forward-like’’ operator that mixes the composite signal with a smoothed causal derivative term. The resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover. An application to high-frequency EURUSDT (1-minute) illustrates that causally constructed observables can exhibit substantial economic relevance in specific regimes, while degrading under subsequent regime shifts, highlighting both the potential and the limitations of causal signal design in non-stationary markets.

Keywords: Causal Inference, Time Series Forecasting, Kalman Filter, Microstructure Features, Non-Stationary Markets, Foreign Exchange

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical tools such as Kalman filtering, causal derivative approximations, and stochastic process theory, indicating high math complexity. It also demonstrates empirical rigor through application to real high-frequency EURUSDT data with realized returns and turnover evaluation, though it stops short of presenting full backtest code or exhaustive parameter optimization.

  flowchart TD
    A["Research Goal: Construct Causal Observable<br>for Non-Stationary FX Forecasting"] --> B{"Data Input:<br>High-Freq EURUSDT 1min"}
    B --> C["Key Methodology Steps"]
    C --> C1["Causal Centering &<br>Micro-feature Aggregation"]
    C1 --> C2["Kalman Filter<br>Stabilization"]
    C2 --> C3["Forward-Like Operator<br>Adaptive Mixing"]
    C3 --> D["Computational Process:<br>Interpretable Decision Functional"]
    D --> E["Key Outcomes:<br>Economic Relevance in Regimes<br>Limitations under Shifts"]