Performance-Driven Causal Signal Engineering for Financial Markets under Non-Stationarity

Abstract

We introduce a performance-driven framework for constructing strictly causal forward-oriented observables in strongly non-stationary time series. The method combines a robustly normalized composite of heterogeneous indicators with a causally computed derivative component, yielding a local phase-leading effect that is amplified near regime transitions while remaining fully causal. A hysteresis-based decision functional maps the observable into discrete system states, with execution delayed by one step to preserve strict temporal ordering. Adaptation is achieved through a walk-forward scheme, in which model parameters are selected using rolling train--validation windows and subsequently applied out-of-sample. In this setting, the validation segment acts as an internal performance screen rather than as a statistical validation set, and no claims of generalization are inferred from it alone. The framework is evaluated on high-frequency financial time series as an experimentally accessible realization of a non-stationary complex system. Under a controlled zero-cost setting, the resulting dynamics exhibit a pronounced risk-reshaping effect, characterized by smoother trajectories and reduced drawdowns relative to direct exposure, and should be interpreted as an upper bound on achievable performance. These results illustrate how causal signal engineering can generate anticipatory structure in non-stationary systems without relying on non-causal information, explicit horizon labeling, or high-capacity predictive models.

Figures (9)

• Figure 1: Pipeline overview. Prices are mapped to indicators, causally normalized, aggregated into $F_0(t)$, and transformed into a forward-oriented observable $F(t)$ via a gated derivative term. A hysteresis rule produces the binary exposure state, evaluated under a walk-forward protocol.
• Figure 2: Causal robust normalization applied to four technical indicators (MFI, RSI, BB%, and MACD) for EURUSDT (left) and BTCUSDT (right). Top row: centered indicators, $\tilde{I}^{(k)}_t = I^{(k)}_t - m^{(k)}_t$, where $m^{(k)}_t$ denotes the causal rolling median computed over a 5000-minute window. Middle row: robust local scale estimates $s^{(k)}_t$, obtained as the rolling Median Absolute Deviation of the centered series. Bottom row: normalized indicators, $Z^{(k)}_t = \tilde{I}^{(k)}_t / s^{(k)}_t$ (dimensionless), mapped to a common dimensionless scale, enabling direct comparison and aggregation across indicators.
• Figure 3: Relationship between the composite indicator $F_0(t)$ (gray), its non-causal advance $F_0(t+6)$ (blue), and the horizon-based trend indicator $\Delta^{(10)}(t)$ (red). The advanced signal exhibits alignment with the horizon trend, particularly around zero-crossings associated with local regime transitions. Lower panels illustrate the corresponding sign-based regime markings used for visualization.
• Figure 4: Median magnitude of the constructed signal, $\mathrm{median}(|F(t)|)$, as a function of the gating parameters $(\lambda_1,\lambda_2,A)$, computed over the last 100,000 observations for EURUSDT and BTCUSDT. The derivative parameters are fixed at $n_{\text{diff}}=2$ and $w_{\text{ma}}=2$. The smooth and monotonic dependence indicates that the gating parameters predominantly determine the scale of $F(t)$.
• Figure 5: Rolling window schedule used for causal walk-forward model selection. At each epoch boundary $t$, parameters are estimated on a past training block, selected using the immediately preceding validation block, and then executed out-of-sample on the next block. We impose $w_{\text{exec}}=w_{\text{val}}$ so that the validation horizon matches the operational trading horizon, enabling directly comparable performance metrics.