Papers

Stock price prediction remains challenging due to the non-stationary and noisy nature of financial time series. Existing deep learning models often rely on rigid decision-level fusion, ad hoc hyperparameter tuning, and compressed final-layer outputs, causing information loss, overfitting, and limited cross-market generalization. We propose VertiFuseX, a hybrid LSTM architecture using penultimate-layer vertical fusion of multi-scale temporal representations. VertiFuseX stacks and reweights penultimate features from LSTM, Bi-LSTM, and St-LSTM branches, integrates a parallel DNN stream, and jointly optimizes all components via backpropagation under a fixed hyperparameter configuration. This preserves richer intermediate temporal information across scales. Evaluated on 15 years (2010-2024) of closing prices from 10 global equity indices using strict chronological out-of-sample testing with the final 365 trading days held out, VertiFuseX achieves 30-54% MAPE reductions and over 40% improvements in MAE and RMSE versus LSTM-based baselines, and outperforms seven state-of-the-art models across 33 metric-dataset comparisons. Ablation studies confirm penultimate-layer fusion drives these gains over final-layer fusion and decision-level ensembling. Gradient-based saliency analysis shows consistent emphasis on mid-range dependencies at lags 9-15 days. Economic validation via algorithmic trading simulation under extreme market regimes shows reduced maximum drawdowns and superior risk-adjusted returns. With 675k parameters, a 2.6 MB memory footprint, and 1.5 ms/sample inference latency, VertiFuseX offers a lightweight, interpretable, deployment-ready framework for robust financial forecasting.

Commodity futures are shaped by harvest cycles, weather shocks, storage conditions, and seasonal demand, but it remains unclear whether recurring patterns yield robust out-of-sample trading profits. Existing research documents return seasonality in commodity futures as well as more complex seasonal structure, while leaving less evidence on how alternative seasonal models compare under common implementation constraints. This article compares dummy-variable regression (DVR), Singular Spectrum Analysis (SSA), and robust low-rank SSA (RLSSA) within a unified trading framework, including a volatility-normalised specification. Using monthly delivery-avoidance returns for 15 liquid commodity futures, the models are estimated on rolling ten-year windows and evaluated from 2016 to 2024 with transaction costs, an equal-weight long benchmark, and Maximum Entropy Bootstrap (MEB) assessment. Across 500 MEB paths, the benchmark has the strongest average full-period profile, with a cumulative return of 16.81%, a Sharpe ratio of 0.191, and a maximum drawdown of -0.414. Classical SSA has the strongest average model outcomes, but negative median cumulative returns and deep drawdowns indicate substantial path sensitivity. Volatility normalisation reduces the average DVR short loss but generally weakens SSA-based portfolios. None of the 18 approximate paired MEB Sharpe tests rejects after within-family Holm adjustment. Because MEB preserves each contract's temporal rank ordering, the assessment is conditional on observed timing rather than a timing-randomised seasonal null. The evidence does not establish robust benchmark outperformance and shows that model performance varies materially across market subperiods.

Constructing a confidence interval for the difference between two independent binomial proportions involves a nuisance direction that is not identified by the estimand. The one-sample Wilson score interval inverts a scalar score test, but has no direct bivariate analogue isolating the difference: inverting the joint normal approximation yields an elliptical region in the unit square, whereas the estimand \(p_1-p_2\) is one-dimensional. We define the Elliptically Optimal (EO) confidence interval as the range of \(p_1-p_2\) over this region and solve the resulting optimization problem in closed form, obtaining explicit bounds in six mutually exclusive and exhaustive cases. The solution admits a compact characterization: the EO interval is the score interval obtained by maximizing over the nuisance variance rather than estimating it. It is therefore the shortest interval obtained by projecting the elliptical region, and inherits its coverage guarantee. We derive the exact coverage excess, \(2[\Phi(z\mathcal{R})-\Phi(z)]\), where \(\mathcal{R}\) is the ratio of the least-favourable to the true standard deviation. The excess vanishes on an explicit line through the parameter space, is bounded by \(\alpha\), and is invariant under proportional scaling of the sample sizes. Exact enumeration of the binomial coverage shows that the Wald interval, whose variance estimator is downward biased by a factor \(1-1/n\) under balanced allocation, falls below nominal coverage almost everywhere. The EO interval never under-covers under the normal approximation and always yields admissible, non-degenerate bounds. Its price is over-coverage when both proportions are extreme, which we quantify exactly.

The Log S-fBM model, introduced by Wu et al., is a stochastic volatility model whose log volatility is a stationary fractional Brownian motion (S-fBM): a stationary Gaussian process with power-decaying autocovariance driven by the Hurst exponent $H$, and variance scaled by an intermittency coefficient. A key property is that it reconciles rough volatility, where $H$ is typically near $0.1$ (see Gatheral et al.), with multifractal volatility, where $H$ is close to $0$ as in Bacry, Muzy et al.: the model's volatility measure converges to a multifractal random measure as $H\to0$. Numerical findings in Wu et al. show intermittency of order $0.02$ across financial assets, motivating a small intermittency approximation of log volatility moments for calibration via the general method of moments (GMM). In this work, we conduct a statistical analysis of the Log S-fBM model. We derive scaling properties of the S-fBM process and the Log S-fBM integrated volatility measure, present deviation inequalities with tail distributions sensitive to $H$ and intermittency, and develop a hypothesis test for the null Hurst exponent, i.e.\ rough versus multifractal dynamics. Finally, we revisit scale invariance of the log volatility increment process via explicit small-intermittency formulas, reproducing analogous properties in both regimes.

MASTER's inter-stock multi-head attention – the module responsible for modeling cross-sectional stock relationships – accounts for 42.5% of model parameters and 25% of predictive value. We systematically decompose this module and uncover a surprising structure: the learned attention is near-uniform (perplexity 278/300), yet forcing exact uniformity eliminates all cross-sectional discrimination. Spectral analysis resolves this paradox: the deviation from uniformity is low-rank (effective rank ~65, top-10 modes capture 96.5% of energy), explaining why sparse approximations consistently fail while Nystrom low-rank attention (m=32 landmarks) matches full O(N^2) attention at O(mN) cost – certified equivalent via TOST at both N=300 (5 seeds, Rank IC p=0.003) and N=800 (10 seeds, Rank IC p=0.034). Additional findings include: (i) attention anti-correlates with return similarity (Spearman rho = -0.614; on the industry-labeled subset, -0.645 unconditionally and -0.627 after controlling for industry, beta, and volatility), suggesting complementarity-seeking rather than correlation mining; (ii) all graph-based alternatives degrade performance, with hard masking worse than complete module removal; and (iii) at N ~ 3,500 with adapted architectures, no cross-stock module (GCN, Nystrom, or MASTER-style pipeline) significantly outperforms a per-stock LSTM baseline (n=4 seeds), indicating that the benefits observed at smaller scales do not trivially transfer. These results establish that the inter-stock attention's value resides in a compressible, dynamic, near-global redistribution that rewards low-rank approximation but resists sparsification.

We build and evaluate a pre-game win-probability forecaster for individual maps (“games”) in professional League of Legends (LoL). The proposed model is a one-stage logistic regression fit end-to-end on the win/loss log-loss: each team's exponentially-weighted moving average of past same-side results, a ridge-shrunk stable strength that is the maximum-a-posteriori estimate of a logistic mixed model, and a first-pick draft covariate, natively calibrated out of sample (walk-forward slope $0.995$). It augments a purely dynamic Bradley–Terry specification with stable team strengths. A second, independently built two-stage composite mixed model under restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) shrinkage, with Platt calibration, serves as the strongest rival the authors could build. On $5{,}135$ games across six regional leagues and three international events (2024–2026), under paired per-game Diebold–Mariano inference, the two architectures are statistically indistinguishable on every protocol and window (global holdout $0.2230$ vs.\ $0.2257$; walk-forward $0.2207$ vs.\ $0.2215$), so the simpler model is preferred on parsimony, not accuracy; both improve on the classical dynamic benchmark ($0.2351$) by a clear margin and on the static fits ($0.2301$/$0.2268$) more modestly. Against Polymarket on $928$ matched maps, the forecasts are statistically indistinguishable from the market on its own per-game contracts, with a modest market edge concentrated on cross-region Worlds and series-decider maps.

Financial markets alternate between periods of relative stability and instability, with structural breaks marking the transitions between these regimes. Identifying such breaks in real time is a central requirement for any trading or risk system operating at high frequency. This report studies Bayesian Online Changepoint Detection (BOCPD) and two extensions proposed in the literature, and applies them to the signed order flow of NASDAQ-listed equities.

We develop a filter for time series, defined at each time $t$ as the minimizer of a discounted convex combination of observed and expected losses. The filter can be estimated by simulation to an arbitrary level of accuracy in $O(1)$ flops at each time point $t$ and can be run for all values $t=1,...,T$ in parallel. These methods are applied to robustly compute a preaveraged price process from the more than 1.5 million trades made on a single financial asset in a single day where the noise's variance is infinite. It yields a flat "volatility signature" plot, down to the 1 second level, so the microstructure noise no longer biases the volatility estimate. This is not true when linear methods are employed.

We introduce ALM-GARCH, an asymmetric long-memory GARCH model in which positive and negative innovations enter conditional variance with different injection amplitudes and kernel offsets. These departures define testable level and memory channels relative to a nested symmetric benchmark. Positive Harris recurrence holds for interior configurations under a Foster-Lyapunov condition. Across five equity indices and Bitcoin, joint symmetry is rejected throughout, driven primarily by the level channel. The memory channel is supported for the Nikkei 225, KOSPI, and Bitcoin but is weakly identified when the positive branch is nearly inactive. Out-of-sample performance is broadly comparable to standard benchmarks.

Investment performance is commonly presented either as a conventional cumulative-return chart, which fixes a historical starting date and traces performance forward, or as a trailing-return table, which fixes the current endpoint but reports only a small set of prespecified horizons. These two displays have complementary limitations: fixed-start comparisons are conditional on the selected origin, whereas trailing returns provide only discrete snapshots of the underlying fixed-endpoint return function. We present the Return-to-Present (RTP) curve as a continuous fixed-endpoint representation that brings these perspectives together by holding the evaluation date fixed while allowing the hypothetical historical purchase date to vary over the available history. Familiar 1-month, 3-month, 6-month, 1-year, and longer trailing returns therefore become selected points on a continuous curve. When multiple investments are overlaid, RTP directly displays entry-date sensitivity, persistent relative advantage, crossings, and the timing and magnitude of separation without requiring selection of a single historical origin. The same endpoint-based construction naturally accommodates investments with unequal inception dates, recurring purchases, and retrospective portfolio rotation decisions in which sale and replacement-purchase dates may differ. We illustrate these uses with real investment data and discuss its relationship to momentum. RTP does not define a new return measure; its contribution is a simple graphical organization of familiar realized returns for historical comparison and decision support rather than prediction or statistical inference.

Let a finite population of n labelled examples carry a class-weighted loss, with pi*n in a rare positive class weighted by N0/N1. We study estimation of total risk from a subsample K << n under designs allocating K0 and K1 draws to the two strata. We derive the exact finite-population variance of the weighted risk estimator under class-conditional sampling without replacement and solve for the optimal allocation. The class multiplier inflates positive-stratum dispersion by the imbalance ratio, causing that ratio to cancel from the optimal allocation and making equal, rather than proportional, allocation the natural default. Simple random sampling is dominated by an explicit between-stratum term; an exact bias identity shows that cluster-representative selection has no general unbiasedness guarantee; and a Serfling bound transfers the allocation result to selection error over a finite candidate set. Under the implemented truncation, the realised allocation ratio is gamma=min(2*pi/f,1), independent of n, yielding the parameter-free efficiency prediction A(pi,f)=gamma/[pi(1-pi)(1+gamma)^2]. A separate measurability result bounds the record occupied by a labelled example, determining the required train-test separation and controlling departure from block independence under absolute regularity. We test these predictions on forecasting the onset of statistically explosive price regimes, dated ex post by the Phillips-Shi-Yu procedure, using 350 U.S. equities from 2004-2011 with under 1% positive rows and five purged forward blocks. The predicted ordering of the four designs holds, and at the 10-day horizon the five design points are ordered exactly as predicted by A (Spearman rho=1, exact p=0.0167). The predicted dependence on pi across horizons does not hold; we identify the channels lying outside the design-based argument.

Validating a model on a time series asks for three things at once: each training run should use most of the sample (sufficiency), the test sets should together cover most of the sample (coverage), and training data should come before test data (causality). We prove that the three cannot be had together and price each one. Let $\alpha$ be the smallest training fraction over folds, $\beta$ the fraction of the sample covered by tests, $\Lambda$ the fraction of the sample used as training data from the future of a test point, and $\delta$ the distance from a test point to the nearest training point in its future. Every scheme on a sample of length $T$ satisfies $\alpha+\beta \le 1+\Lambda$ and $\alpha+\min\{\beta,\delta/T\} \le 1$, and under $\beta$-mixing the leakage bias at a test point is at most $2M\beta_{\mathrm{mix}}(\delta)$. In words: going beyond the causal frontier $\alpha+\beta=1$ requires training on the future; that future data must sit within $(1-\alpha)T$ of a test point; and its harm depends on its distance, not its amount. Hence expanding walk-forward is exactly the Pareto frontier of causal validation, $k$-fold cross-validation buys the most future data, and purged $k$-fold with an embargo pays in distance instead, which is cheap when the process forgets quickly but cannot repair the part of causality demanded by non-stationarity. On pure noise, shuffled 5-fold reports an information coefficient of $+0.32$, while contiguous 5-fold, using the same amount of future data, reports $+0.004$.

Trade durations in high-frequency foreign exchange data exhibit increased occurrence near integer values. To address this empirical phenomenon, we propose the granularity-adjusted autoregressive conditional duration (GA-ACD) model. It is based on a novel two-component mixture distribution consisting of a standard generalized gamma component for regular durations and a second component that locally redistributes probability mass around integer values to capture heaping. Conditional dynamics are modeled within a score-driven framework, allowing the scale parameter to vary over time in response to past durations, and enabling maximum likelihood estimation of all model parameters. A simulation study shows that ignoring heaping leads to biased parameter estimates and distorted inference regarding both the distribution and the dynamics of durations. An empirical analysis demonstrates that integer-duration clustering is pervasive across major currency pairs and that the GA-ACD model outperforms the standard generalized gamma ACD model.

Recent advances in LLM agents enable a new paradigm for asset pricing, which we call Agentic Empirical Asset Pricing (AEAP): systems that autonomously conduct the scientific discovery process itself. We define AEAP and identify its core building blocks. Existing evaluation practices backtest only the outputs (factors or trades), not the autonomous discovery system that produced them. We focus on factor discovery, contributing a reference architecture, a rigorous evaluation standard for discovered factors, and a method for out-of-sample backtesting the discovery system. As a concrete instance of that architecture, we evaluate SEADS against five re-implemented baselines on two US equity panels using this standard: no single metric ranks the systems consistently, motivating evaluation on multiple axes at once. A separate rolling re-execution then asks the complementary question of whether the discovery process itself, not one static output, is reliable. We also report negative findings and limitations that surface further evaluation pitfalls for future AEAP systems.

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20% and increases the Sharpe ratio by approximately 40% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9% Model Confidence Set that retains only the neural estimator.

Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-level distribution-valued characteristics can instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed from Qwen3-Embedding-8B news representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reported frozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.

Spatial asset-pricing models take the structure of inter-firm interaction as given. We infer that structure from firms' information environments using language-model representations. Each firm is represented as a distribution of news-article embeddings, and a target-anchored Wasserstein barycentric reconstruction selects, for every firm, the weighted combination of other firms whose information footprints jointly reconstruct its own. The resulting directed peer field enters a quadratic exposure-adjustment model in which the spatial coefficient indexes alignment with information peers relative to stand-alone exposure. Using fields built from 2018-2022 news and frozen before 2023-2026 returns, we find that the constructed field organizes cross-sectional return dependence beyond the Fama-French five factors and momentum and raises the held-out mean Gaussian quasi-log score relative to a matched factor-only model. Because factor betas are unchanged, the gain lies in residual covariance. The field outperforms pairwise distance weighting and equal weighting of the same peers, and remains incrementally informative beside persistent news co-mentions under the primary factor-conditioned specification. Linear and quadratic transport generate nearly identical peer-return signals and equivalent held-out predictive performance. The barycentric-proximity ordering persists across alternative embedding models, and a pre-period encoder preserves the held-out advantage under the primary specification. Language-model representations thus serve as a measurement instrument for latent inter-firm information structure in capital markets.

Classical option-hedging methods like Black-Scholes delta assume constant, free rebalancing, which real markets don't allow. Deep hedging trains a neural network to handle these frictions directly, and prior work reports strong results. But those comparisons usually pit deep hedging against a frictionless classical baseline on simulated price data. That's not a fair fight, and it leaves open whether the advantage is real. We test this using five years of actual BTC options data from Deribit (2020-2024), comparing Black-Scholes delta, Leland's cost-adjusted hedge, and the Whalley-Wilmott no-trade band against three deep hedging setups: an LSTM and a feedforward network, each trained with a CVaR loss and, in some runs, a penalty for trading too often. All six strategies face the same 5 basis point transaction cost. On 11,546 test episodes from September 2023 to December 2024, Whalley-Wilmott cuts transaction costs significantly versus hourly rebalancing, saving $1.79 per episode against plain BS delta (95% CI [-2.21, -1.39], p < 0.0001) by trading about eight times less often. Its P&L and tail-risk numbers are better too, though not quite significant at this sample size. None of the three deep hedging models beat any classical benchmark on any metric, and all kept trading almost every hour regardless of penalty weight, a twenty-fold range barely moved the needle. A calmer validation period shows Whalley-Wilmott's P&L edge shrinks or disappears there while its cost edge holds, so the result depends on market regime. We think the likely causes are a small training set and the lack of any built-in mechanism for sitting still in the architectures tested. Not a flashy result, but an honest one: a real-data check on a claim mostly supported by simulations so far.

Large language models (LLMs) are increasingly used to discover trading strategies, and much of the resulting literature shares a methodological weakness: many candidate strategies are generated, the best is reported, and neither look-ahead bias nor the intensity of the search behind the reported result is corrected for. We present a strategy-discovery system that makes both corrections structural rather than procedural. First, the agent can only act through registry-validated tools whose feature space excludes look-ahead by construction; we show that this guardrail is not redundant with statistical correction: a deliberately leaky oracle posting a Sharpe ratio of 35 survives Deflated Sharpe and probability-of-backtest-overfitting testing completely. Second, the system records every strategy evaluation its search performs and deflates all reported performance by that trial count, tracing how the best in-sample Sharpe ratio climbs with each trial while the deflation threshold, driven by the agent's own search, climbs faster. Across a 453-stock point-in-time US equity universe and a 39-ETF multi-asset universe with realistic transaction, impact, and borrow costs, honest evaluation certifies passive benchmarks (out-of-sample confidence intervals excluding zero), rejects every LLM-discovered strategy (across two frontier models, search budgets up to one hundred candidates, and five repeated runs), catching selection luck, predicted rank degradation, and out-of-sample collapse through complementary instruments, and evaluates a human trader's production rule system under identical instruments. The framework formalizes why pre-registered hypotheses earn lower evidential bars than brute search, and quantifies the sample sizes that credible certification of moderate edges actually requires.

This paper develops the first end-to-end application of cross-sectional learning-to-rank to the S&P 500 weekly options (SPXW) zero-day-to-expiration surface, integrated with margin-aware position sizing, an abstention rule driven by model uncertainty, and a strict out-of-time integrity check. A LightGBM LambdaRank ranker scores a daily nine-strategy cross-section composed of eight delta-targeted short-put positions and a SKIP candidate, trained against a path-aware Sortino-on-bars label computed at one-minute resolution. The framework is evaluated under index-option margin requirements, a tiered fee schedule, and bid-to-mid execution assumptions across a four-window walk-forward over 2021-2024 and a strictly held-out 2025 out-of-time slice. Seven sizing methods produce out-of-time annualized Sharpe ratios between 4.31 and 5.76, with the headline method reaching a Probabilistic Sharpe Ratio of 0.964 and a sample-period maximum drawdown of -2.28%, on a single hold-out year against a walk-forward range of 1.90 to 3.11. Out of time, every method exceeds three passive benchmarks (CBOE PUT, CBOE WPUT, SPX buy-and-hold) by at least 3.84 in Sharpe ratio and five internal selection baselines by at least 3.69. A two-by-two ablation of the confidence gate against the tail-risk features places 5.05 of the 5.59 out-of-time Sharpe gap over the CBOE PUT with the ranker and the selection layer, the two risk controls adding 0.54 between them. On walk-forward, where the gate binds, neither control comes close to the headline alone and their interaction supplies most of the result. A fifteen-group feature ablation shows that removing the multiplicative regime interactions collapses walk-forward statistical confidence.

Lead-lag relationships are widely used in financial time series, and many clustering algorithms based on them have been developed. The traditional DTW-KMedoids algorithm performs well both on the synthetic dataset and the real financial dataset. However, there are still several limitations to these algorithms: low efficiency caused by high time complexity, poor mathematical properties from DTW distance, the clustering effect is sensitive to the number of clusters. To solve the problems above and improve the performance, this paper introduces three clustering algorithms: MiniRocket-KMeans, KShape, Ensemble algorithm (a combination of KShape and DTW-KMedoids) and compares their performance on synthetic and real stock datasets with DTW-KMedoids algorithm under the same trade strategy. In addition, this paper also finds the best number of clusters by maximizing the silhouette coefficient in each clustering algorithm to improve the stability of the experiment results. Our main conclusions are as follows: MiniRocket-KMeans performs best under the lead strategy, achieving a Sharpe ratio of 0.866 with a maximum drawdown controlled at -63.9%; the ensemble algorithm exhibits excellent stability; the robustness is significantly improved after finding the best number of clusters; the p-values of the hypothesis test on the Sharpe ratio of all strategies are 0.0, verifying the statistical validity of the lead-lag trading strategy. Finally, future improvement directions such as customized lead-lag matrices and optimized ensemble voting mechanisms are proposed.

Backtests of trading strategies are often selected after many parameter trials. A strong historical result can therefore reflect search luck rather than a persistent signal. Standard summaries such as return, Sharpe ratio, and drawdown do not record how many candidates were tried, whether the selected rule survives out-of-sample validation, or whether the available history is long enough to support the result. This paper describes the MinervaScore, a post-selection robustness grade for trading strategies. The score combines four established validation quantities: Deflated Sharpe Ratio, Probability of Backtest Overfitting, Superior Predictive Ability, and Minimum Track Record Length, with a regime-stability diagnostic. These components are converted into signed margins from their admissibility thresholds, aggregated into a raw score, and then mapped to a 0-100 display. The display is tied to a binary Robustness Seal: scores of 80 or higher are shown only when all five gates pass. The calibration uses 359,062 production backtest records. The score is intended to rank statistical support, not to estimate the probability of future profit. In synthetic markets with known ground truth, the MinervaScore separates true signal from lucky backtest outcomes, with an AUROC of 0.989 at the headline difficulty. Its improvement over the GT-Score proxy and the gates-passed baseline is modest, and it remains close to the corrected DSR-alone baseline. In a pre-registered test on unseen real-market data, the score showed no significant forward relationship in a population with limited surviving edge (Spearman rho_s = 0.013, one-sided permutation p = 0.40). We therefore present the MinervaScore as an auditable validation and reporting layer, rather than as evidence of demonstrated real-market predictability.

In this paper we propose a new formulation of the Bayesian Filter as used in the discrete-time Markov-Switching-Multifractal (MSM) model of volatility based on existing permutation symmetry within the likelihood structure. We show both analytically and empirically that such a formulation leads to a reduction in time complexity from $O(D^k)$ to $O(k^D)$ thereby significantly reducing the computational bottleneck associated with dimensionality. We compare the agreement between the naive and sector filters and find that while there are significant disagreements, the ground-truth recovery of the latter seems to improve on the former.

At 15-minute horizons, directional mean reversion is far stronger and more pervasive in cryptocurrency markets than in US equities: scored under one matched, strictly out-of-sample protocol, 90% of 183 Binance pairs carry significant directional reversal against 2.7% of 187 US stocks and ETFs, in every focal coin-year since 2021. The signal lives in signs, not magnitudes: lag-one return autocorrelation is near zero on the major coins, yet simply betting against the previous candle captures most of the effect. US-listed funds whose net asset value is a crypto or metal price inherit their underlying's reversal, including its absence, from their first months of trading; stocks merely correlated with the same underlyings inherit nothing: descriptive evidence that a wrapper's tape reads like the process it wraps, not the venue it prints on. On the originating tape, the reversal concentrates after moves driven by aggressive taker flow and grows with flow intensity, while the order-book depth a move consumes conditions nothing: a conditioning consistent with compensated liquidity provision, not a test that selects it. The gross edge peaks near 1.3 bp per trade against a 5 bp round-trip cost: large enough to detect, too small to clear benchmark spot capture costs. The contrast survives an artifact battery, an exact permutation null, and a frozen six-month holdout, with a class-mean AUC gap of +0.031 as designed and +0.011 (95% CI [+0.008, +0.014]) under the most conservative accounting, clear of zero either way.

Option-implied rates are often treated as frictionless because completed boxes deliver riskless payoffs. I show that this interpretation requires option- and benchmark-side implementation wedges to offset. Using SPX and RUT options from 2012-2025, I find a 2-3 bp unannualized increase in the option funding basis when maturity first crosses December 31. The effect behaves as a fixed price wedge, strengthens in the mid-2010s, survives alternative contracts and benchmarks, appears independently in government-bond CIP, and is reproduced in an independently constructed option panel. Put-call parity can identify discount rates precisely without establishing their economic purity.

Tests of conditional mean independence can lose power when departures are confined to a bounded part of a multivariate predictor space and the relevant spatial scale is unknown. We propose a Multiscale Ball Conditional Mean Independence (MBCMI) test that aggregates support-weighted local mean contrasts in an outcome variable across balls centered on each data point in a predictor set. Fixed-grid theory identifies the population target, establishes consistency for grid-visible alternatives, and derives a Pitman local-power limit governed by the ball-smoothed mean departure. For serial data, feasible recursive-sign-bootstrap validity for stable finite-order autoregressions with conditionally sign-symmetric innovations is established. Application-aligned serial null experiments reject 4.25% of the time. MBCI is demonstrated to be strongest for local and radial signals. Predictor-law experiments show that these conclusions are not an artefact of independent Gaussian covariates. In monthly U.S. finance data, cross-fitted residual MBCMI tests remove every full-sample rejection, suggesting contemporaneous conditional-mean dependence rather than evidence of distinctive nonlinear structure.

Hedge ratios, factor models and diversified portfolios all rest on an estimate of which firms move together. That estimate is not stable: firms migrate between the groupings the market treats as coherent, and when enough migrate the organizing axes of the cross-section turn. We measure the rate of that turning as the mean squared sine of the principal angles between subdominant eigenspaces of consecutive twelve-month S&P 500 correlation matrices. A typical month rewrites a fifth of the structure and carries four-fifths forward. That rate is priced: it couples to the aggregate variance risk premium at t = 5.40, no level measure correlates above 0.32, and the implied-correlation surface spans at most 6.7 percent of it. Only the persistent component is priced - the premium compensates the pace of revision, not the distance traveled. The mechanism is prepayment: implied variance rises on impact, volatility follows two to three quarters later (simulated-null p < 0.03 at h = 1-9), and the premium converges as it arrives. Three pre-registered boundaries hold: no timing alpha, no crash protection, and a downside version inseparable from intensity. The premium is, in part, rent on exposure held over a map still being redrawn.

Human capital is a central organizational input, but standard financial data reveal little about firm-specific disruptions to workforce availability, cost, skills, and continuity. I construct a measure of disclosed human-capital disruption from earnings calls using author-defined coding criteria and a contextual language model. Within firms, a one-standard-deviation increase in the annual measure is associated with 0.55 percentage points higher idiosyncratic volatility, 0.58 percentage points higher downside deviation, and a 0.46 percentage point lower worst monthly return, with no corresponding relation to market beta. The results are stable across seven broader and narrower classification rules and remain after removing explicit labor-shortage passages and controlling for a recently published labor-shortage measure and transcript-wide negative and uncertain language. At the call level, human-capital disruption predicts approximately 0.50% higher idiosyncratic volatility over the following 42 trading days after conditioning on pre-call risk. Risk is elevated before the call as well, and the score predicts the continuation of that firm-specific risk state over the following 42 trading days. After telegraphing and succession passages are removed, the measure also predicts subsequent named-executive roster exits and the incumbent CEO's effective departure from office. Earnings calls therefore reveal disturbances to a key organizational input that are broader than labor shortages and informative about the distribution of firm outcomes.

Using neural networks for stock return prediction typically requires choices about depth and hidden-layer width that are difficult to connect to financial interpretation. We study an alternative: estimate dependence among firm characteristics with a Maximally Filtered Clique Forest (MFCF), then map its clique structure to a Homological Neural Network (HNN). The MFCF maximum clique size K is the only parameter controlling architectural complexity, and it has a clear graphical meaning: it bounds the number of characteristics in each maximal clique and hence the highest interaction order the network can represent. The filtered graph then fixes the neural network's depth, layer widths, and sparse connections before training, in place of a separately chosen depth and width sequence. We apply two HNN variants to annual out-of-sample forecasts of U.S. stock excess returns from 1987 to 2016 using 94 firm characteristics. The HNN models match a three-hidden-layer benchmark on pooled predictive accuracy, rank the cross-section more accurately, and use roughly 80 times fewer parameters than a fully connected network with the same induced layer widths. Two structural ablations indicate that both the sparse connectivity and the estimated grouping of characteristics contribute to the ranking advantage, and both effects remain significant after correcting for multiple testing. These findings show that HNNs offer a practical and interpretable way to incorporate estimated dependence among firm characteristics into neural architecture design.

Two old market sayings hold that news is already priced in by the time it is published, and that the rumor is bought while the news is sold. Both place the price move associated with a piece of news before and at publication rather than after it. Whether the claims hold, for which kinds of news, and by how much are basic questions about how fast markets absorb public information. We test them on 4.57 million financial news articles covering roughly 3,000 US stocks (2023-2026). A large language model teacher, distilled into a compact classifier through active learning, assigns each article one of 17 event tags and five attributes; articles are clustered into stories to separate first reports from follow-up coverage; and beta-adjusted abnormal returns are measured around the resulting 1.68 million stock-day events, with 364,405 neutral-sentiment events as a placebo group. Three results follow. First, the price move associated with news concentrates before and at publication: pooled across all signed events, the cumulative move in the news direction by the close of publication day is 2.8 times its value 20 days later, and for rumor-flagged events the rumor day captures the entire move while the subsequent confirmation contributes nothing. Second, measured against the placebo of comparable stocks, markets underreact to numbers and overreact to stories: quantified fundamental news (earnings, dividends, guidance, analyst actions) keeps drifting in the direction of the news for weeks, while soft story-driven news (launches, macro commentary, leadership) gives back its move. Third, news carries width as well as direction: publicity raises volatility before the publication day, and volatility declines once the news is out, because publication resolves uncertainty. The study also produces a table of measured drift for each event tag, usable as a prior in news-conditioned forecasting models.