All technical indicators are first mapped to a common dimensionless scale through a two-step causal transformation based on rolling medians and Median Absolute Deviation (MAD). Let wnorm denote the normalization window.

It is worth noting that the indicators selected for this work differ in scale: RSI, MFI, and BB% operate within a fixed range of [0, 100], facilitating a uniform interpretation. By contrast, the MACD has no predefined bounds and scale proportionally to both the asset price and its volatility. See Appendix A for details. For each indicator It (k) and for t ≥ wnorm, define the causal window

t(ωnorm ) = {τ: t − wnorm ≤ τ < t}.

containing the wnorm observations strictly prior to t. The causal rolling median (baseline) is m( tk) = median {Iτ (k):τ ∈ t(ωnorm )}.

and the centered series is

I ˜t (k) = It (k) − m( tk).

A robust local scale is obtained via the causal MAD on the centered series:

st (k) = median {|I ˜τ (k)| : τ ∈ t(ωnorm )} + ε

where ε > 0 is a small constant preventing division by zero. Both m( tk) and st (k) depend only on past data (τ < t), ensuring strict causality. The normalized indicator is then

(k) (k)

(k) It − mt Zt = (k) . (1) st This transformation yields a scale-free and outlier-robust representation of each indicator. All subsequent steps operate exclusively on the normalized series {Zt (k)}, ensuring that differences in scale or volatility do not dominate the composite signal.

Given the normalized indicators {Zt (k)}, we define a composite observable as a convex linear combination:

F0(t) = ∑ αkZt (k), (2)

where αk ≥ 0 and ∑K k=1 αk = 1. This construction preserves the dimensionless nature of the normalized indicators and yields a composite signal interpretable as a consensus Z-score.

In this study, the aggregation weights are fixed and chosen uniformly, αk = 1/K. This design choice is deliberate. By holding the weights constant, we isolate the effect of the causal normalization, derivative-based enhancement, and regime gating mechanisms, reducing the risk of overfitting and improving interpretability. Allowing the weights to vary or be optimized is a natural extension of the framework and is left for future work. We employ four market indicators1: Zt (RSI), Zt (MFI), Zt (BB%), Zt (MACD) whose formal definitions are provided in Appendix A. Each component captures a distinct aspect of market behavior: RSI measures momentum extremes, MFI incorporates volume-weighted pressure, BB% encodes volatility-adjusted price location, and MACD reflects trend acceleration. Their aggregation into F0(t) produces a multi-dimensional consensus signal. Coherent deviations across indicators reinforce the composite magnitude, while idiosyncratic noise from individual indicators is attenuated. This structure provides a stable foundation for the forward-oriented transformation introduced in the next subsection.

The causal robust normalization introduced in Section 2.1 maps each indicator into a dimensionless representation that is stable under non-stationarity and suitable for linear aggregation. Fig. 2 illustrates this transformation for the four indicators used in this study (RSI, MFI, MACD, and BB%) on EURUSDT and BTCUSDT, using a 600-minute excerpt of one-minute data. The normalization window is set to wnorm = 5000 minutes, balancing statistical robustness against adaptation to evolving market conditions. The top row shows the centered indicators, obtained by subtracting a causal rolling median. This step removes slow-

1 Throughout this work, “MACD” refers to the MACD histogram (i.e., the difference between the MACD line and its signal line), and “BB%” denotes the Bollinger %B indicator, also commonly referred to as %b in the technical analysis literature.

moving baselines and aligns all series around zero. In raw units, however, the indicators operate on markedly different numerical scales: RSI, MFI, and BB% are bounded by construction, whereas the MACD is scale-dependent, as it is defined as a difference of moving averages of the underlying price. For EURUSDT, prices are of order unity, and the associated moving averages therefore remain close to one. Consequently, the MACD signal naturally lies at a much smaller scale, of order 10−4, reflecting relative price variations rather than absolute levels. The middle row reports robust local scale estimates computed via the causal MAD. Since the MAD is not scale-invariant, the smaller values observed for the MACD reflect its lower numerical scale rather than reduced dynamical variability. In this example, the BB% exhibits the largest dispersion, followed by the MFI and the RSI.

After normalization (bottom row), all indicators fluctuate on comparable, dimensionless scales. Expressed as deviations from a local median in units of robust local variability, each component contributes symmetrically to the composite observable F0(t), preventing dominance by any single indicator and ensuring meaningful aggregation under non-stationarity.

To incorporate forward-oriented structure while preserving strict causality, we define a derivative-enhanced observable F(t) from the composite signal F0(t). Let ndiff denote the lookback window used to compute causal finite differences, and let wMA be a short smoothing window applied to the resulting difference series. The discrete causal derivative is defined as

(ndifr ) F0(t) − F0(t − ndiff ) ∂t F0(t) = , ndiff where ndiff ≥ 1 is the window length instead of the order of differentiation. Unlike the unit-lag differencing operator employed in ARIMA models (see Wilson [13] and Hamilton [14]), which is primarily designed to

Top row: centered indicators, ̃ It (k) = It (k) − m( tk), where m( tk) denotes the causal rolling median computed over a 5000-minute window. Middle row: robust local scale estimates st (k) , obtained as the rolling MAD of the centered series. Bottom row: normalized indicators, Zt (k) = Ĩ( tk)/s( tk) (dimensionless), mapped to a common dimensionless scale, enabling direct comparison andaggregation across indicators.

remove stochastic trends and enforce stationarity, the present operator uses a finite backward difference overan extended horizon to extract slope information that is informative about near-future signal evolution. The resulting quantity approximates the local rate of change of F0(t) based exclusively on past observations. To reduce high-frequency noise, the derivative series is further smoothed via a causal moving average MA of length ωMA,

∂ ̃ tF0(t) = MAw [∂(ndirr )F0],

MA t

The forward-oriented observable is then defined as

F(t) = c1(t)F0(t) + c2(t) ∂ ̃ tF0(t), (3) with state-dependent mixing coefficients

c1(t) = tanh(|λ1F0(t)|) ; c2(t) = A[1 − tanh(|λ2F0(t)|)], where λ1, λ2 > 0 control sensitivity to the magnitude of the composite signal and A > 0 sets the overall scale of the derivative contribution. In strongly persistent regimes, where |F0(t)| is large, the coefficient c2(t) is suppressed and F(t) behaves similarly to the level signal F0(t). Conversely, near transition regions (F0(t) ≈ 0), the derivative term is emphasized, yielding a causal approximation to a small forward shift of the composite signal. The derivativeinduced phase advance is illustrated in Appendix B. The operator does not forecast future values; it mixes level and slope information in real time. The link to horizon-based trend objectives is discussed in Section 2.5.

The forward-oriented operator F(t) is designed to causally anticipate changes in the trajectory of the composite indicator F0(t). This objective is closely related to the notion of trend persistence and regime duration that underpins a large body of empirical work in financial economics. Seminal contributions by Pagan and Sossounov [15] and Lunde and Timmermann [1] formalize market trends as bull and bear phases and study their statistical properties ex post, including the duration dependence of regime termination. Our approach shifts the focus from ex-post classification to ex-ante anticipation. We construct a causal signal that responds early to structural changes in market dynamics. Empirically, the non-causal advance F0(t + 6) exhibits strong alignment with a forward-looking price-based trend metric, suggesting that the composite indicator contains information relevant to future regime transitions.

To formalize the trend target used in the literature, consider a price series {Pt} and define the horizon-based future and past price averages as

H H−1

fut 1 past 1 μH (t) = ∑ Pt+i, μH (t) = ∑ Pt−i.

i=1 i=0

The corresponding horizon-based percentage trend indicator is then given by (H) μfut H (t) − μpast H (t) Δ (t) = past , (4) μH (t) which contrasts the average future price over the next H periods with the average past price over the preceding H periods. This construction, or close variants of it, is widely used as a benchmark for identifying local trend direction and strength.

Fig. 3 illustrates the empirical relationship between the contemporaneous composite signal F0(t), its non-causal advance F0(t + 6), and the horizon trend indicator Δ(10)(t). Despite being derived from distinct sources, F0(t + 6) and Δ(10)(t) exhibit similar zero-crossing behavior, suggesting that advancing F0 by a small number of steps captures information relevant for horizon-based trend objectives. Naturally, F0(t + 6) is not available in real time and cannot be used operationally.

The two lower panels provide an illustrative mapping from these signals to directional regimes, shown side by side on a shared time axis. For simplicity, buy (green) and sell (red) regions are defined by sign changes of the respective signals, i.e., crossings of a zero reference level. This visualization is intended solely to highlight the similarity in regime timing induced by the two constructions and to serve as a conceptual bridge to the explicit decision rules introduced in the next section.

The derivative component in the forward-oriented operator F(t) provides a causal mechanism to approximate this anticipatory behavior. This approximation implicitly assumes that the composite signal F0(t) admits a locally smooth evolution, e.g., is locally Lipschitz-continuous over the relevant time scale, so that a first-order expansion provides a meaningful description of its short-horizon dynamics. Since ∂tF0(t) captures the local rate of change of the composite signal, a first-order expansion yields

F0(t + δ) ≈ F0(t) + δ ∂tF0(t). (5) showing that a suitably scaled derivative term can emulate a small forward shift. In our construction, the adaptive gating coefficient c2(t) effectively implements a regime-dependent δ, amplifying the derivative contribution near transitions and suppressing it during strong trending phases.

Although a fixed multi-step advance (e.g., six periods) is impossible under strict causality, the derivativeenhanced signal F(t) acts as a causal surrogate for limited forward anticipation. This provides a direct conceptual link between the proposed signal construction and horizon-based trend targets widely used in the literature. The economic relevance of this surrogate is ultimately assessed through the PnL-driven walk-forward optimization described in Section 2.8.

The forward-oriented observable F(t) serves as the primary input to a binary decision rule. Let st = F(t) denote the signal value at time t. A position state pt ∈ {0, 1} is maintained, where pt = 1 corresponds to a long position and pt = 0 to a flat (cash) position.

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.

To mitigate noise-induced whipsaws, state transitions are governed by a hysteresis mechanism with threshold θ > 0:

1, if pt−1 = 0 and st > +θ, pt = {0, if pt−1 = 1 and st < −θ, (6) pt−1, otherwise.

This design ensures that a switch from flat to long occurs only when the signal surpasses a positive threshold, while a switch from long to flat requires the signal to drop below a negative threshold. The neutral zone between −θ and +θ prevents excessive trading when the signal oscillates near zero.

For a strictly causal implementation, the position state used to compute returns at time t is the previous state pt−1. Let rt = (Pt − Pt−1)/Pt−1 be the simple return of the underlying asset. The strategy return at time t is then:

Rt = pt−1 ⋅ rt. (7)

The cumulative equity curve is obtained by compounding:

Vt = V0 ∏ (1 + Rτ). (8)

With V0 = 1 as the initial capital. Trading activity is quantified by the total number of position changes over a given horizon T:

Turnover(T) = ∑ |pt − pt−1|. (9)

Before introducing the parameter optimization framework, we examine how the scale of the constructed signal F(t) depends on the gating parameters. This analysis is essential because trading decisions are based on thresholding F(t): the frequency of trades and effective exposure depend on how often |F(t)| exceeds a decision threshold θ. If the amplitude of F(t) varies substantially with (λ1, λ2, A), jointly optimizing these parameters together with θ becomes ill-posed, as distinct configurations may generate similar trading behavior through simple rescaling. Characterizing the dependence of the signal magnitude on the gating parameters is therefore necessary to decouple signal construction from decision calibration.

To isolate gating effects, we fix equal indicator weights αk = 1/K and compute F(t) over the last 100,000 observations (approximately 70 days of one-minute data) for EURUSDT and BTCUSDT. Price data consist of one-minute OHLCV series obtained via the Binance public Spot API [16]. The sample spans January 2022 to December 2025. Missing candles are handled by forward-filling prices and setting volume to zero, ensuring a regular time grid without introducing look-ahead bias.

The derivative parameters are fixed at ndiff = 2 and ωma = 2. For each experiment, one gating parameter is varied while the others are held constant, and the signal scale is summarized by median (|F(t)|).

Fig. 4 shows a smooth and monotonic dependence of the signal magnitude on the gating parameters. Increasing λ1 raises median (|F(t)|) by strengthening the level component, while increasing λ2 suppresses the derivative contribution and reduces the overall amplitude. The parameter A scales the derivative channel almost linearly. These patterns are consistent across both assets, indicating that the robust normalization of F0(t) stabilizes the baseline scale, whereas (λ1, λ2, A) primarily control the effective amplitude of F(t).

The derivative parameters are fixed at ndiff = 2 and ωma = 2. The smooth and monotonic dependence indicates that the gating parameters predominantly determine the scale of F(t).

Additional experiments (not shown) indicate that moderate variations around ndiff = 2 and ωma = 2 do not materially affect the structure or scale of F(t) relative to the dominant influence of the gating parameters. This separation motivates treating the decision threshold θ independently of signal-shaping parameters. The next section introduces the walk-forward optimization framework and describes how θ is selected in a manner consistent with the observed scaling behavior of F(t).

Given the forward-oriented signal F(t) and the decision rule defined in Section 2.6, the trading strategy depends on a finite set of parameters that govern both signal construction and temporal adaptation. For clarity, we partition these parameters into two groups.

I. Signal construction parameters, which determine the shape and scale of the forward-oriented observable F(t). II. Walk-forward window parameters, which control how the model adapts to non-stationarity over time.

The signal construction parameters are collected in

Θsig = {ndiff . wma . λ1. λ2. A}. (10) where ndiff and ωma define the causal derivative operator, and (λ1, λ2, A) govern the adaptive gating mechanism introduced in Eq. (3). Threshold selection is treated separately (See Section 3.2) to avoid confounding signal scaling with execution filtering. The walk-forward protocol introduces two additional window parameters,

Θwin = {ωflt, ρ}, (11) where wfit denotes the length of the training window and ρ determines the validation horizon via ωval = ⌊ωfit/ρ⌋. The out of sample execution window is set equal to the validation window (wexec = wval), ensuring a consistent evaluation horizon across epochs, as detailed in Section 2.9.

At each walk-forward epoch, the parameter set optimized is therefore

Θ = Θsig ∪ Θwin.

The optimization is performed via a discrete grid search over predefined candidate values. The specific grids employed in the empirical analysis are reported in Table 1.

Objective function. For a given parameter configuration Θ, the pipeline generates a sequence of strategy returns {Rt(Θ)}T t= eval 1 . The terminal profit-and-loss over the evaluation window is

Teval

PnL(Θ) = ∏ (1 + Rt(Θ)) − 1. (12)

Assuming unit initial capital. Here, Teval denotes the number of observations in the evaluation block on which the objective is computed. To enable comparisons across evaluation windows of different lengths, we maximize the time-normalized objective

PnL(Θ) J(Θ) = ,

Because the objective J(Θ) is evaluated through a fully causal backtest, gradient information is unavailable and parameter selection is performed via black-box optimization. To respect nonstationarity while preserving strict causality, we adopt a walk-forward protocol in which estimation, model selection, and execution are explicitly separated in time. In this protocol, the “validation” block serves purely as an operational performance filter that ranks candidate configurations based on recent behavior; it is not interpreted as an independent hold-out set providing formal guarantees about future generalization.

At each epoch, the data are partitioned into three contiguous past-to-present blocks (see Fig. 5):

I. A training block of length wfit, used exclusively for signal construction and state estimation.

II. A validation block of length wval, used solely for internal model selection and short-horizon monitoring, it is not used to report performance and does not constitute an out-of-sample test.

III. A subsequent test/forecast block of length wexec, on which the selected strategy is executed out-of-sample. At an epoch boundary t, these blocks are defined as

train: [t − ωftt − ωval, t − wval). (14) val: [t − ωval, t). (15) test: [t, t + ωexec ). (16) Crucially, parameter selection never uses information from the test block. The parameter vector Θ is chosen by maximizing the validation score computed exclusively on the validation block:

Θ∗(t) = arg max Jval(Θ; ωval), (17)

where denotes a finite grid of candidate configurations (see Table 1). The selected configuration Θ∗(t) is then frozen and applied without modification to the subsequent test block, producing the out-of-sample position sequence used to construct the global equity curve. A schematic overview of the rolling trainvalidation execution schedule, including the enforced horizon constraint ωexec = ωval, is shown in Fig. 5.

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 ωexec = ωval so that the validation horizon matches the operational trading horizon, enabling directly comparable performance metrics.

In addition to optimizing Θ, the protocol allows the window lengths (ωfit, ωval, ωexec) themselves to vary across epochs. Operationally, this is implemented as a discrete search over wfit and a ratio parameter ρ, which determines the validation length via

ωftt

ωval = round ( ρ ). (18)

We impose the constraint

ωexec = ωval, (19) which ensures that model selection and out-of-sample execution are evaluated over identical horizons. This constraint serves three purposes; 1) it enforces a clear separation between estimation and execution while maintaining a consistent evaluation scale, 2) it reduces the effective dimensionality of the window search, mitigating the risk of horizon overfitting, and 3) it yields a transparent operational interpretation in which the trading horizon is calibrated on the most recent validation period and immediately deployed on the next unseen block of the same duration. Under this walk-forward scheme, the loop advances in steps of wexec, producing non-overlapping out-of-sample test blocks whose concatenated positions define the global equity. At this point, it is useful to contrast the present framework with earlier heuristic constructions in the literature. That study can be recovered as a particular and more restrictive instance of the current construction, with simplified preprocessing and empirically chosen, fixed hyperparameters. Related approaches based on derivativeaugmented indicators have been explored in prior work (see, [12] e.g.,), but without the robust normalization and systematic walk-forward calibration introduced here. Aggregation weights were adjusted to yield signals of similar visual amplitude, and key hyperparameters– including the derivative gain, smoothing horizon, and mixing coefficients–were selected empirically based on qualitative inspection and preliminary performance.

While this heuristic approach proved effective and provided early evidence of the benefits of derivativeaugmented signals, it lacked an explicit normalization scheme, a principled calibration procedure, and a unified parameterization across indicators. The present work addresses these limitations by introducing robust MADbased normalization, a formally defined composite signal scale, and a systematic walk-forward calibration of all hyperparameters. Under this formulation, the framework of [12] emerges as a special case obtained by fixing the normalization to simple centering and selecting constant parameter values, thereby situating the earlier results within a broader and more robust causal signal engineering paradigm.

All stages of the pipeline indicator processing, normalization, signal construction, parameter selection, and trading execution are strictly causal, relying exclusively on information available up to time t. To isolate the intrinsic behavior of the signal construction and decision mechanism, all results reported in this section are obtained under zero transaction costs. This choice allows us to analyze the raw statistical and dynamical properties of the strategy independently of market-specific frictions, which are addressed in a separate robustness analysis.

Under the walk-forward framework introduced earlier, at each rebalancing time t, model parameters are estimated through a train–validation split relying exclusively on historical information (Section 2.8), after which they are held fixed and applied out-of-sample over a contiguous test window. The global equity curve is constructed by concatenating the corresponding out-of-sample position paths across successive windows. The walk-forward optimization framework described in Section 2.8 was implemented with the following parameter grids:

These parameter ranges were selected based on preliminary sensitivity analyses (Section 2.7) to cover a wide but computationally tractable search space. The fixed values for ndiff and ωma reflect the minimal configuration that provides stable derivative estimates while preserving high-frequency signal dynamics.

The hysteresis threshold θ governs regime transitions in the final trading The choice is closely related to the empirical scale of the constructed signal. Fig. 4 characterizes how the typical magnitude of the forward-oriented observable F(t) varies as a function of the gating parameters, summarized through median (|F(t)|). This analysis identifies a natural signal scale of order unity across assets and parameter configurations. Operating directly at the level of the median signal magnitude would, however, result in excessive regime switching. Since |F(t)| exceeds its median value by construction approximately half of the time, setting θ near the median would induce frequent threshold crossings and a high turnover trading regime dominated by short-lived fluctuations. From a trading perspective, the hysteresis threshold must therefore be chosen above the typical median scale in order to enforce regime persistence and suppress noise-driven transitions. Accordingly, we consider a discrete set of threshold values

θϵ{0.6, 0.8, 1.0, 1.4, 1.6}, which spans values below, near, and above the median signal magnitude reported in Fig. 4. This range allows us to study the sensitivity of trading behavior to the degree of hysteresis while remaining within a scale-consistent operating regime.

Importantly, the interpretation of Fig. 4 does not rely on forward-looking information. While the figure is computed over a long sample for descriptive purposes, additional diagnostic checks (not shown) indicate that the empirical distribution of |F0(t)| and in particular its high percentiles remains remarkably stable over time for both assets considered. This temporal stability implies that the characteristic scale of the signal is a structural property of the normalization and aggregation procedure, rather than an artifact of a specific market phase or sample endpoint.

Figure 6 reports the out-of-sample walk-forward performance of the proposed strategy for EURUSDT and BTCUSDT under zero transaction costs. For each asset, the figure compares the cumulative return of the proposed strategy across different values of the threshold parameter θ with a Buy-and-Hold benchmark, and displays the cumulative number of executed trades over time.

Strategy versus Buy-and-Hold for different values of θ, and the cumulative number of executed trades. The equity curves reveal distinct but economically meaningful effects across assets. For EURUSDT, the proposed strategy exhibits sustained growth and consistently outperforms Buy-and-Hold across a wide range of θ values. For BTCUSDT, although Buy-and-Hold attains a higher terminal return for some thresholds, the proposed strategy produces markedly smoother equity curves, with visibly reduced drawdowns and lower path variability.

The lower panels of Fig. 6 show that trading activity differs across markets, reflecting differences in volatility and regime dynamics rather than changes in signal construction, which is identical across assets. Importantly, variations in trading frequency across θ do not translate into increased instability of the equity process. Even in the more volatile BTCUSDT market, the strategy maintains controlled exposure and avoids the large drawdowns observed under Buy-and-Hold.

To quantify these qualitative observations, Table 2 reports risk and return metrics for Buyand Hold and for the proposed strategy evaluated at the selected threshold value θ∗ = 1.0. This choice is not motivated by a maximization of out-of-sample performance. Rather, θ∗ = 1.0 provides a convenient and interpretable reference point at which trading activity, regime persistence, and signal magnitude are all clearly expressed, facilitating the analysis of parameter distributions, trade statistics, and regime behavior.

Importantly, the qualitative conclusions drawn in the subsequent sections do not depend on this specific value. As illustrated in Fig. 6, alternative threshold choices lead to predictable changes in trading intensity but preserve the core behavior of the strategy.

Performance is computed by concatenating out-of-sample test windows across the full sample, with risk, drawdown, and activity metrics reported for θ∗ = 1.0. All metrics are computed at the native one-minute frequency. Sharpe and Sortino ratios are reported in non-annualized form. For comparison with annualized benchmarks, these ratios can be scaled by √365 × 24 × 60. For standard definitions of the reported performance metrics, see, e.g., Bacon [21].

Taken together, the results indicate that the proposed framework primarily acts as a risk-reshaping mechanism. By combining causal signal construction, adaptive derivative leading, and hysteresis-based execution, the strategy systematically transforms raw market exposure into a smoother equity process sacrificing part of the upside in highly volatile environments while delivering strong absolute and risk-adjusted performance in more stable regimes.

Beyond aggregate performance and risk metrics, the temporal structure of trading regimes provides insight into the economic nature and practical viability of the proposed strategy. In particular, the distribution of position holding times reveals whether performance is driven by sustained regime identification or by rapid oscillations more likely associated with microstructure noise.

Fig. 7 reports the empirical distribution of non-flat position durations (measured in one-minute candles) for EURUSDT and BTCUSDT under the selected walk-forward configuration. Each duration corresponds to a contiguous interval during which the strategy maintains a long position before reverting to flat.

Both assets display highly asymmetric duration distributions, characterized by a concentration of short holding times (on the order of tens of minutes) and a long right tail extending to several thousand minutes. This structure is consistent with frequent local regime fluctuations coexisting with less frequent but persistent directional phases. Despite substantial differences in volatility and market microstructure, the qualitative shape of the duration distributions is remarkably similar across EURUSDT and BTCUSDT. This similarity suggests that the forwardoriented causal signal extracts regime information in a manner that is robust across asset classes, rather than being tuned to idiosyncratic price dynamics.

Table 3 summarizes key descriptive statistics of the position durations. The median holding time is approximately 22–23 minutes for both assets, while the upper quantiles reveal the presence of materially longer regimes. In particular, the 90th percentile lies around 77 minutes, and the maximum durations exceed 10,000 minutes in both markets, indicating that the strategy intermittently locks into persistent regimes. Both assets exhibit strongly rightskewed distributions, with a large mass of short-lived positions and a non-negligible tail of persistent regimes.

From a practical perspective, the prevalence of short-duration positions highlights the importance of transaction costs and execution frictions. Since all results are reported under zero transaction costs, the observed performance should be interpreted as a measure of the signal’s informational and regime-detection content, rather than as a directly tradable outcome.

At the same time, the presence of a non-negligible tail of long-duration positions indicates that the strategy is not merely exploiting high-frequency noise. Instead, it intermittently captures persistent regimes, precisely the environments in which transaction costs are less dominant and economic value is more likely to survive realistic execution conditions.

To provide a compact view of the tuning behavior induced by the walk-forward selection procedure, summarizes the empirical frequency with which each hyperparameter value is selected as optimal across epochs, separately for assets. Rather than reporting a single best configuration, these histograms reveal which regions of the search space are repeatedly preferred by the out-of-sample validation criterion, hence offering an interpretable diagnostic of hyperparameter stability under non-stationarity.

The top panels report the distribution of the rolling-window lengths used by the walk-forward protocol: the training window length wfit, wpred and the validation partition ratio ρ. In our experiments, wval = wpred. The bottom panel reports the distribution of the selected values for the signal-construction parameters.

Each bar reports the number of epochs in which a given value is selected as optimal, shown separately for EURUSDT and BTCUSDT.

All indicators are computed using exclusively information available up to time t, ensuring strict causality, and follow standard definitions widely used in empirical finance and technical analysis (see Appel [22] and Murphy [23] for details). The indicators {Zt (k)} are summarized in Table 4, together with their economic interpretation and defining equations. Each indicator captures a complementary aspect of market dynamics, as briefly summarized below.

Table A1. Technical indicators used to build the composite observable F0(t).

Indicator Range Definition RSI [0,100] 1 100 × ൬1 − ൰ 1 + Gt/Lt MFI [0,100] 1 100 × ൬1 − ൰ 1 + PMFt/NMFt

MACD diff. Scale-dependent ( EMA fast − EMA slow )t − Signal t BB% [0,100] Pt − (μt − kσt) 100 × ቆ ቇ (μt + kσt) − (μt − kσt)

RSI, MFI and BB% are bounded in [0, 100], whereas MACD is scale-dependent. The Relative Strength Index (RSI), following Wilder [24], measures the balance between recent gains and losses and provides a bounded representation of short-term momentum. The Money Flow Index (MFI) extends this concept by incorporating traded volume, thereby capturing buying and selling pressure beyond price movements alone [23]. The MACD difference reflects changes in trend intensity by comparing short- and long-horizon exponential moving averages and their signal line [22]. Finally, the Bollinger Band Percent (BB%) expresses the relative position of the price within a volatility envelope, yielding a dimensionless measure of price extremeness conditional on recent volatility.