From Dot-com to AI: drawdown onsets prediction in AI technology stock market

Financial markets periodically experience sharp and apparently sudden changes (Ang and Timmermann, 2012), with multiple supposedly rare and extreme events recurring over the past 2 decades. The question at hand is therefore not how often those events occur, but whether they are genuinely unpredictable or possible to anticipate, specifically in the accelerating AI technology sector.

Predicting these shifts remains a complicated endeavour. Most approaches frame it as binary classification, which overlooks distributional shifts (Guan and Tibshirani, 2022) and class imbalance in financial networks (An et al., 2025). A signal in the vicinity of the drawdown starting point is operationally just as valuable for hedging and position management as pinpointing the exact onset, yet standard metrics penalise early warnings equally with misses.

We propose an Iterative Market Understanding and Generation Inference (IMUGI) framework – a multilayered predictive system for assessing the probability of drawdown onset, inspired by regime-switching early-warning models, Hawkes-type jump clustering, and meta-learning architectures that ensemble heterogeneous predictors.

Throughout this paper we distinguish two concepts. A drawdown (DD_t) is the cumulative percentage decline from a historical peak; it is critical when it falls in the worst 20% of its empirical distribution. A crisis event is a temporal episode constructed by clustering consecutive days of extreme drawdowns. Our prediction target is the drawdown start date. We test the framework on a composite AI stock index of 27 US-listed technology companies spanning 2003–2025.

Understanding what precedes major drawdowns requires building on a set of theoretical foundations, from crash physics and bubble mechanics to regime-switching models and early-warning systems.

Sornette's (2009) Dragon King theory positions extreme crashes as mechanistically distinct outliers arising from identifiable phase transitions, diagnosable ex-ante via LPPL modelling — with predictive validity demonstrated across several historical crashes (Johansen and Sornette, 2010) and confirmed across six independent systems (Sornette and Ouillon, 2012) — in contrast to Taleb's (2007) view of crises as inherently unpredictable. Consistent with both, financial returns exhibit fat tails incompatible with Gaussian assumptions (Mandelbrot, 1963; Mandelbrot and Hudson, 2004; Nolde and Zhou, 2021), motivating reliance on Student-t emissions throughout our framework:

where each regime k has its own location vector μ_k and scale matrix Σ_k, estimated via EM, while the degrees-of-freedom parameter ν—which governs tail heaviness (ν → ∞ the distribution converges to the Gaussian)—is shared across regimes and fixed at ν = 5. The use of conditional Student-t distributions in hidden Markov models is established in the literature (Bulla, 2011), and the ν = 5 is consistent with recent empirical work showing it minimises the kurtosis gap for equity return distributions without degrading distributional fidelity (Alswaidan and Varner, 2026).

Asset bubbles are the primary phenomena through which severe drawdowns emerge. Cognitive biases and herd behaviour drive speculative buying beyond fundamental value, aligned with Keynesian “animal spirits” theory (Akerlof and Shiller, 2009), while rapid price appreciation, excessive leverage, and credit expansion provide observable warning signals (Jordà et al., 2015). Scheinkman and Xiong (2003) formalised the mechanism: when short-sale constraints relax, accumulated pessimism is gradually incorporated into prices, producing sustained post-restriction declines — the dot-com bubble (1995–2000) being the canonical illustration (Ofek and Richardson, 2003).

Drawdown-based rules serve as risk-reduction techniques in asset selection (Van Hemert et al., 2020) and drawdown-based optimisation (Chekhlov et al., 2005). The Financial Crisis Observatory and the Hyped LPPL model translate bubble diagnostics into trading strategies delivering annualised returns around 34% on equity indices, providing direct empirical evidence of economic gains from crash-onset signals (Cao et al., 2025).

IMUGI integrates five strands established in previous literature: bubble physics and log-periodic power-law (LPPL) modelling (Johansen et al., 2000; Sornette, 2003; Jordà et al., 2015; Sornette et al., 2015), regime-switching and hidden Markov models (Hamilton, 1989; Ang and Bekaert, 2002; Guidolin and Timmermann, 2007), self-exciting Hawkes processes (Hawkes, 1971; Filimonov and Sornette, 2012; Blanc et al., 2017; Chen et al., 2024), empirical crisis prediction and early-warning systems — from leading-indicator models (Kaminsky et al., 1998; Berg and Pattillo, 1999; Bussière and Fratzscher, 2006; Frankel and Saravelos, 2012; Schularick and Taylor, 2012; Drehmann and Juselius, 2014) to time-to-event/survival specifications (Cox, 1972; Shumway, 2001) — and heavy-tailed, jump, and extremal-event analysis, including extreme-return contagion (Engle and Manganelli, 2004; Embrechts et al., 1997; Mandelbrot, 1963; Bae et al., 2003; Nolde and Zhou, 2021). Prior work within each strand addresses these problems in isolation, typically relying on macroeconomic predictors or single-mechanism specifications; IMUGI combines all five using market microstructure features.

Existing ML approaches (Ghasemieh and Kashef, 2022; Tölö, 2020; Rao and Rojas, 2025; Zhao et al., 2025) share a common failure: optimising for retrospective state identification rather than prospective onset prediction, with detections concentrated near the deepest drawdown point — after the institutional hedging window has closed. The Hyped LPPL model (Cao et al., 2025) suggests that mechanistic priors add predictive value, though this does not constitute proof that Dragon King dynamics are the operative driver. IMUGI addresses these gaps by combining bubble physics, regime memory, and self-excitation within a single online probabilistic architecture (Appendix B, Figure 5).

The AI technology index is a market-capitalisation-weighted composite of 27 NASDAQ-listed technology companies with significant AI exposure (see Appendix A, Table 10).

The constituents were selected as the set of NASDAQ-listed firms with identifiable revenue or strategic exposure to AI-relevant activities — semiconductors, cloud infrastructure, enterprise data platforms and AI-native software — as identified at the index construction date. The index is intended to represent the population over which AI-sector overvaluation dynamics are defined, in line with the paper's prediction target. Market-cap weighting downweights recently listed firms in earlier periods, leaving training-period index dynamics dominated by established large-cap technology firms. While this structural weighting mitigates but does not eliminate survivorship and hindsight-driven selection concerns (Brown et al., 1992), the index should be read as representing the AI technology sector as currently identified.

The index spans January 2003 to October 2025 (22.8 years; 5,742 trading days). Daily adjusted closing prices and shares outstanding for all constituents were retrieved via the yfinance API (Aroussi, 2019). Index construction follows the dynamic divisor methodology standard in contemporary index design (S&P Dow Jones Indices, 2022).

First, at the baseline date (January 1st, 2003), the total market capitalisation across all constituent companies is computed. A fixed divisor is calculated as:

where Base Value = 1,000. Second, on each trading day t, the index value is calculated as the sum of each stock's price multiplied by shares outstanding, divided by fixed divisor:

where P_i(t) is the adjusted closing price and S_i is the shares outstanding for company i. This market-cap-weighted approach ensures that larger constituents have proportionally greater influence on index movements, reflecting the concentration characteristic of the AI sector.

Evaluation requires an identification of crisis drawdown events. Following an adaptive distribution-based methodology, major drawdowns are detected via the following procedure:

Let P_t denote the price of the AI technology index at time t. Define the drawdown series in accordance with Chekhlov et al. (2005) as:

Days on which DD_t lies in the worst 20% of its empirical distribution (20th percentile) are initially flagged as crisis days. Consecutive runs of crisis days, allowing for short gaps of up to 10 trading days, are merged into single candidate crisis episodes; episodes shorter than 3 days are discarded as noise. For each remaining episode, the crisis anchor is defined as the date within the episode at which DD_t attains its minimum (maximum peak-to-trough loss).

The 20th percentile threshold is aligned with the results of Kaminsky et al. (1998), that were selected via optimisation to minimise the noise-to-signal ratio of crisis signals. The 20th percentile threshold is further grounded in the drawdown literature: Van Hemert et al. (2020) demonstrate that in a 10-year window with typical risk characteristics (10% volatility, 0.5 Sharpe ratio), there is a 43% probability of hitting a −20% maximum drawdown, yet only 9.9% probability of exceeding −30%. This positioning of the 20% threshold as a natural boundary between recoverable volatility and systemic distress provides empirical support for the current selection.

For each valid crisis episode, two key dates are attributed: the start date, defined as the most recent high-water mark before the anchor,

and the anchor date, t_anchor, the date of maximum loss during the episode. The primary prediction target is the drawdown start date, i.e. the onset of the correction from its peak. Binary labels for model training and evaluation are constructed by marking an anticipation window of 9 trading days preceding each identified drawdown start as positive (y_t = 1), with all other periods marked as negative (y_t = 0).

To assess whether the empirical conclusions depend on the event-definition choices, we conducted a local sensitivity analysis around the baseline specification. In addition to the main 20th-percentile drawdown threshold, robustness checks are performed at the 15th and 25th percentiles. Hence, the binary anticipation window is varied across 5, 9, and 15 trading days. This design preserves a common event-detection framework while testing whether predictive performance is stable under variations in drawdown severity.

Analysis of the AI technology index (constructed from 27 NASDAQ constituents, 2003–2025) identified 12 unique drawdown onsets generating 17 distinct crisis events. This multiplicity reflects protracted multi-stage declines where intermediate recoveries create multiple local minima from a single peak. Three onsets exhibit clustering, Table 1 documents all events.

Drawdowns exhibit heterogeneous morphologies: flash corrections (21–29 days, −13.52% to −27.71%), intermediate declines (48–184 days, −14.45% to −26.53%), and protracted crises (311–821 days, −14.31% to −53.86%). Figure 1 illustrates this heterogeneity and reveal multi-stage dynamics with oscillations before final trough depths. The presence of multiple anchors per onset demonstrates that large drawdowns do not follow simple one-stage declines; instead, they exhibit oscillations and recovery attempts before reaching the lowest depths. This complexity validates the SOHMM framework's design for real-time discrimination of distinct crisis regimes.

To operationalise the drawdown driving mechanisms identified in the literature – positive feedback loops, log-periodic precursors, jump clustering, volatility amplification, and multivariate regime breakdowns – eight features spanning LPPL bubble physics, microstructure dynamics, and extremal phenomena were computed for daily inference.

Three LPPL-derived indicators are adapted from Sornette et al. (2015) with modifications for non-stationary AI stock dynamics and drawdown detection at the 20th-percentile threshold. Rather than Sornette's 126 linearly-spaced windows, we use 15 logarithmically-spaced windows for computational efficiency while retaining coverage across three economically meaningful regimes: long-term hype cycles (600–750 days), medium-term institutional adoption (300–500 days), and short-term retail momentum (125–200 days):

The LPPLS model fitted to normalised log-prices is:

where t_c is the critical time (predicted drawdown onset), m ∈ (0.1, 0.9) the power-law exponent, ω ∈ (6, 13) the angular frequency, and ϕ ∈ (0, 2π) the phase, derived from the Johansen–Ledoit–Sornette (JLS) rational expectations model (Johansen et al., 2000; Sornette, 2003).

Rather than Sornette's OLS approach, we employ hybrid optimisation: differential evolution (DE, maxiter = 300) optimises the nonlinear parameters (t_c, m, ω, ϕ) under Huber-robust loss, while linear parameters (A, B, C) are solved analytically within each DE iteration. This combination avoids a six-dimensional nonlinear search and provides robustness to the heavy-tailed shocks common in AI stocks (price jumps of ±15%, corporate actions, liquidity events):

Filtering Constraints Valid windows must satisfy all seven constraints simultaneously (Table 2), derived from the JLS framework (Johansen et al., 2000) and operationalised by Shu and Zhu (2019). Unlike crash-focused formulations that maximise crash probability, our drawdown-specific implementation emphasises sustained decline patterns, relaxing strict oscillatory constraints to isolate gradual structural trend exhaustion rather than the finite-time singularities of Dragon King events.

Damping Constraint and Relaxed Bounds for Non-Stationary AI Markets The damping factor:

derives from Bothmer and Meister (2003), who established damp ≥1 as the condition for a non-negative crash hazard rate in the JLS framework, subsequently operationalised by Shu and Zhu (2019) on Chinese markets and validated by Koistinen (2020) on Finnish equities with 1.4-day average timing accuracy.

For non-stationary AI markets we extend the allowable range to 0 < damp <10: rapid regime shifts, retail-driven herding, and non-stationary intraday microstructure mean that sub-critical damping (0 < damp <1) can coexist with genuine instability signatures.

This relaxation is compensated by the LPPL Trust metric (Section 3.3.1), which detects parameter fragility independently of damping magnitude, retaining the fundamental JLS instability criterion – when market parameters become sensitive to small perturbations the system is approaching a critical transition – without sacrificing sensitivity.

LPPL Probabilistic Proximity Rather than Sornette's theoretical hazard rate $ht=α(tc−t)m−1[1+cos(ω⁡ln(tc−t)−ϕ′)]$⁠, we operationalise drawdown imminence via the LPPLS function's instantaneous log-return at normalised window end (t = 1.0):

where:

The derivative captures both power-law acceleration (−mB term) and oscillatory damping (mC and ωC terms). Sigmoid normalisation maps it to [0, 1]:

Values near 1 indicate accelerating negative returns (drawdown criticality); values near 0 indicate stability or positive momentum.

LPPL Confidence The fraction of windows passing all filtering constraints:

High confidence (≥0.7) confirms that LPPLS signatures persist across temporal scales, reducing false positives from transient noise. Values below 0.5 suggest inconsistent fits, indicating stable or transiently non-stationary regimes. Multi-scale consistency is central to the JLS framework: genuine bubbles exhibit log-periodic oscillations at multiple temporal frequencies simultaneously (Johansen et al., 2000; Sornette, 2003).

LPPL Trust Quantifies parameter robustness via bootstrap resampling (Sornette et al., 2015), with n_bootstrap = 10 resamples (vs. Sornette's 100) for real-time feasibility:

1. Compute residuals $r=Pˆ−P$⁠.

2. Resample with replacement to form synthetic series $Psyn=Pˆ+r*$⁠.

3. Refit LPPLS on each replicate and record whether damp ≥1.

Low Trust $(<0.3)$ indicates parameter sensitivity and dynamical fragility near critical transitions – a hallmark of pre-drawdown regimes where small price changes produce dramatically different parameter estimates. Trust is evaluated against the standard constraint (damp ≥1) independently of the relaxed operational bounds, so it captures fragility even when the main estimate already satisfies damp ≥1.

Five features capture market microstructure dynamics, jump risk, and distributional anomalies, complementing the LPPL indicators. Log return $rt=lnPtPt−1$ stabilises variance (Campbell et al., 1997); return acceleration Δr_t = r_t − r_t−1 serves as a 2–5-day leading indicator of regime inflection points (Sornette, 2003); and annualised 20-day realised volatility $σt=252⋅std(rt−19:t)$ captures time-varying market stress (Andersen et al., 2001). Lee-Mykland jump statistics (Lee and Mykland, 2008) are aggregated across $W={5-10,10-30,30-60}$ days as

flagged at |LMJump_Stat| > 2.58 (α = 0.01) and set to NaN otherwise. Mahalanobis distance (Mahalanobis, 1936; Rousseeuw and Van Zomeren, 1990) is computed over windows {20–30, 30–90, 60–180} days on $xt=(rt,σt,RSIt,MACDt,momentumt,Δrt)T$ as

capturing joint deviations across returns, volatility, and technical indicators during regime shifts. All continuous features are z-score normalised over non-NaN observations; binary indicators retain their {0, 1} form without scaling.

The eight features provide a layered decomposition of crisis morphology: oscillatory bubble accumulation (LPPL indicators), shock self-excitation (LMJump), volatility amplification (rolling volatility), multivariate regime coherence (Mahalanobis distance), and momentum acceleration (return differences). The complete architecture, including feature classes and empirically derived crisis thresholds, is summarised in Table 3.

The SOHMM provides the probabilistic foundation for regime-switching inference in the IMUGI framework. Unlike conventional first-order HMMs, which condition transitions solely on P(S_t∣S_t−1), the SOHMM incorporates trajectory dependence by conditioning on the dyadic state sequence (S_t−2, S_t−1), capturing momentum and mean-reversion patterns that are empirically significant during crisis episodes characterised by pronounced persistence.

The architectural core is the three-dimensional transition tensor $T∈RK×K×K$⁠, K = 5:

A standard first-order HMM uses a single 5 × 5 transition matrix (25 parameters). The SOHMM instead instantiates five matrices A⁽¹⁾, …, A⁽⁵⁾, each conditioned on the regime two steps prior, stacked into a 5 × 5 × 5 tensor (125 parameters). This expansion is economically justified: a crisis regime (k) reached via trajectory (i, j) exhibits fundamentally different forward dynamics than crisis arrival via an alternative path, and the rank-3 structure prevents the rapid state flickering endemic to first-order Gaussian HMMs. The model learns these trajectory-dependent distinctions via the EM algorithm.

The empirical motivation is regime persistence. Define the persistence coefficient for regime c as:

Relative to Nystrup et al.’s (2020) jump-penalised first-order HMM, the SOHMM achieves implicit persistence through trajectory-dependent transitions while additionally capturing momentum and mean-reversion dynamics. A third-order extension (625 parameters) would be ill-identified given only 12 training onsets; the rank-3 structure balances expressiveness with estimability.

The graphical dependency structure is shown in Figure 2: blue arrows represent standard Markovian transitions (t − 1 → t); red dashed arrows capture second-order memory (t − 2 → t).

Initialisation combines K-Means clustering with semantic domain-knowledge scoring in four stages. (1) Global imputation statistics (⁠$x¯d$⁠, σ_d) are computed from training data to fill missing entries. (2) K-Means partitions the imputed data into K = 5 clusters with parameters $μˆk$⁠, $Σˆk$⁠. (3) Each cluster is scored against five target regimes (calm, recovery, euphoria, bubble, crisis) using standardised feature combinations; clusters are then greedily ^[1] matched to regimes by iteratively selecting the highest cluster – regime score – conceptually related to the Hungarian algorithm (Kuhn, 1955) but implemented in simplified form for efficiency. (4) Regime-specific missingness probabilities Ψ_k[d] = P(feature d observed∣state k) are learnt from training data, capturing the MNAR structure (Little and Rubin, 2002).

This hybrid approach is a novel contribution to HMM literature (Rabiner, 1989; Murphy, 2012). The semantic scoring layer encodes domain knowledge (LPPL bubble physics, Hamilton (1989) volatility regimes, Rousseeuw and Van Zomeren (1990) outlier patterns) to guide cluster-to-regime assignment without requiring crisis labels at initialisation, rendering the SOHMM semi-supervised (Chapelle et al., 2006). Labels are reserved for downstream evaluation; the semantic initialisation acts as a soft prior that accelerates EM convergence and improves interpretability under scarce labelled crises.

Static batch-trained models introduce forward-looking bias by implicitly memorising crash patterns during training and then “predicting” those same patterns out-of-sample. We eliminate this circularity via an online learning framework that updates parameters incrementally as observations arrive.

At each time step, model surprise is quantified via KL divergence:

where $γt(k)=P(St=k∣X1t)$ is the posterior and $πt|t−1(k)=P(St=k∣X1t−1)$ is the one-step-ahead predictive distribution. The learning rate is modulated accordingly:

This sigmoid-modulated rate increases under high surprise (enabling rapid adaptation to new regimes) and decreases during stable periods (preserving historical knowledge). The full pipeline—E-Step posterior computation, KL-triggered η_t adjustment, EWMA sufficient-statistic update, and M-Step parameter refinement—is shown in Figure 3, with updated parameters fed back to the E-Step via the state transition tensor $T$⁠. EM convergence criteria, numerical safeguards, and the online damping coefficients (κ_μ, κ_Ψ, κ_Σ) are specified in Appendix C (Algorithms 1–2).

The SOHMM design synthesises HMM fundamentals (Baum and Petrie, 1966; Baum et al., 1970; Rabiner, 1989), multi-order state dependencies (Juang and Rabiner, 1991; Mari et al., 1997), robust Student-t emissions (Peel and McLachlan, 2000), semi-supervised initialisation (Chapelle et al., 2006), and recursive Bayesian filtering (Cappé et al., 2009) into a unified framework adapted for non-stationary financial regimes, heavy-tailed distributions, and MNAR data structures.

Self-exciting point processes model temporal event clustering, where past occurrences elevate future event likelihood. Filimonov and Sornette (2012) demonstrated that price changes decompose into exogenous shocks (background intensity μ) and endogenous feedback (memory kernel), with the Hawkes branching process providing a natural mathematical framework for this decomposition. We adopt this semantic logic and extend the linear Hawkes framework with quadratic interactions to capture multiplicative cascading behaviour during market stress.

Let $E={t1,…,tN}$ denote extreme price move timestamps (returns exceeding the 95th or falling below the 5th percentile of training data). The conditional intensity is:

where τ_i = t − t_i. The seven parameters are: μ (baseline exogenous intensity); α (linear self-excitation); β^diag, β^rank1 (quadratic amplitudes); θ⁽⁰⁾, θ⁽¹⁾, θ⁽²⁾ (exponential decay rates).

Linear kernel (Hawkes, 1971; Bowsher, 2007):

Models standard first-order endogenous feedback, directly analogous to the linear Hawkes term in Filimonov and Sornette (2012).

Diagonal quadratic (Blanc et al., 2017):

Captures local event clustering and microstructure effects within individual event epochs.

Rank-1 quadratic (Sornette, 2003):

Introduces super-exponential scaling: dense event clustering produces intensity spikes through the squared summation, capturing multiplicative cascade effects characteristic of critical market regimes and extending beyond the linear Filimonov–Sornette (2012) framework.

The log-likelihood (Hawkes, 1971; Ogata, 1978) is:

The integral is approximated via the trapezoidal rule with N_quad = 1,000 quadrature points. Parameters are estimated by constrained L-BFGS-B optimisation (Byrd et al., 1995) with a stability penalty (Daley and Vere-Jones, 2008):

This prevents numerical divergence while permitting transient critical bursts. The box constraints and initial values used in estimation are reported in Appendix C (Algorithm 3).

For each calendar date t, the conditional intensity $λ(t∣E≤t)$ is computed using only events strictly before t. Two sequential transformations are applied:

yielding a single normalised feature $h̃Hawkes(t)∈[0,1]$ per date. During testing, the event set $E$ is updated incrementally using the same training-period percentile thresholds, allowing the intensity to reflect accumulated pressure from recent extreme events without look-ahead bias.

The IMUGI framework is a three-layer architecture:

1. A signal layer comprising: a SOHMM for market regime identification; a Q-Hawkes process for extreme-return clustering.

2. A feature layer constructing: five meta-features from SOHMM and Q-Hawkes outputs.

3. A meta-learning layer: a regularised logistic regression mapping the five-dimensional feature vector to a crisis-onset probability.

The SOHMM is trained on eight features: Log Return, Return Acceleration, Volatility, LMJump Stat Detected, MD Avg Outlier, LPPL Proximity, LPPL Confidence, and LPPL Trust. This bundle integrates price momentum, jump detection, outlier intensity, and bubble-formation indicators, enabling discrimination across five latent market regimes while learning state-dependent missing-data patterns via MNAR-aware parameters.

The meta-model uses five features derived from Q-Hawkes and SOHMM outputs:

1. Hawkes $(h̃t)$⁠: normalised Q-Hawkes intensity.

2. SOHMM $(s̃t)$⁠: normalised crisis-transition probability.

3. Hawkes Momentum $(Δ5H=h̃t−h̃t−5)$⁠: five-day change in Hawkes intensity.

4. SOHMM Momentum $(Δ5S=s̃t−s̃t−5)$⁠: five-day change in regime probability.

5. Interaction $(It=h̃t⋅s̃t)$⁠: multiplicative coupling of both signals.

These form the meta-feature vector $xt=(h̃t,s̃t,Δ5H,Δ5S,It)⊤$⁠.

The meta-learner is a regularised logistic regression:

with L2 regularisation and balanced class weights to address the $≈2.5%$ positive label rate.

To benchmark IMUGI against alternatives, we additionally evaluate three external models on the same chronological train–test split: a climatology benchmark that assigns the in-sample event rate to every observation, a discrete-time hazard specification following the logic of Shumway (2001), and a time-varying Cox proportional hazards model (Cox, 1972). Raw benchmark and IMUGI probabilities are converted to calibrated probabilities using isotonic regression fitted on out-of-fold training predictions, with a constant fallback when the training predictions are degenerate, following standard probability-calibration practice (Zadrozny and Elkan, 2002). Model-specific classification thresholds are then selected on the calibrated training predictions by maximising balanced accuracy and are held fixed for the test period. For statistical comparison, discrimination differences in AUC and AUPRC are evaluated on raw test probabilities using a paired moving-block bootstrap with 1,000 replications and 21-trading-day blocks, while calibrated probability accuracy is compared using pointwise Brier loss and a one-sided Diebold-Mariano test with Newey-West variance estimation and the Harvey-Leybourne-Newbold small-sample correction (h = 1) (Harvey et al., 1997).

Due to the LPPL module requiring 750 observations before the first valid estimation window, the effective training sample spans 3,992 trading days (2005-12-22 to 2021-10-01), while the strictly held-out test set spans 999 trading days (2021-10-02 to 2025-10-24). To preserve causal ordering and prevent forward-looking bias, all model fitting, feature preprocessing, calibration, and threshold selection procedures were fixed using training data only, and each prediction for day t was generated using information available up to and including that date. In particular, benchmark-model covariates were imputed and standardised using training-sample quantities only, benchmark and IMUGI probabilities were calibrated using isotonic regression fitted on out-of-fold training predictions, and the benchmark-comparison procedures were then applied unchanged over the test period.

The estimated coefficients of the regularised logistic meta-model are reported in Table 4. Numerically, the intercept is β₀ = −0.2058 and the five slope coefficients are (β₁, …, β₅) = (−6.33, 0.67, 4.68, 3.98, 5.50). The most notable feature is the negative coefficient on Hawkes intensity combined with a large positive interaction term between Hawkes intensity and the SOHMM crisis-transition signal. Substantively, this implies that elevated event-clustering pressure is not interpreted as a crisis warning in isolation, but rather becomes informative when it coincides with elevated regime-instability probability from the SOHMM, which is consistent with regime-dependent interaction effects in self-exciting financial systems (Blanc et al., 2017; Chen et al., 2024).

We first summarise out-of-sample performance on the fixed 999-day test set. Using the pre-specified training-based decision threshold, IMUGI attains an AUC of 0.9055 and a Brier score of 0.1175. Three unique drawdown onsets occur in this window, and Table 5 shows that the framework identifies all three, flagging two in advance and one shortly after onset.

Because these onset-level results rely on only three events, formal inference must be interpreted cautiously. We therefore add two further checks: (1) robustness to alternative crisis-definition thresholds and anticipation windows and (2) comparisons with external benchmark models. Table 6 shows that the 20th-percentile threshold with a 9-day anticipation window is a reasonable baseline. Nearby specifications slightly improve individual metrics but do not dominate across discrimination, calibration, and warning performance. In particular, looser 25th-percentile thresholds worsen Brier loss, while tighter or longer-horizon alternatives reduce either AUC or warning usefulness.

We next compare IMUGI with three external benchmarks. Tables 7 and 8 indicate that IMUGI outperforms all three in ranking-based discrimination and achieves significantly lower calibrated Brier loss in every pairwise comparison.

The AUC margin over Climatology is +0.41 (p < 0.01), confirming that a base-rate model carries virtually no useful timing information for crises. The +0.14 margin over Shumway DTH (p < 0.05) is more informative: because the Shumway model already incorporates time-varying covariates, this gap isolates the contribution of IMUGI's regime-switching and self-exciting components beyond a standard survival framework. AUPRC gains are positive in all three comparisons but reach conventional significance only against Climatology, a pattern consistent with the known conservatism of precision–recall metrics under severe class imbalance (Williams, 2021). Table 8 shows that absolute Brier differences are small $(≤0.0007)$⁠, yet the HLN-corrected DM statistics are large in magnitude (−3.26 to −3.57, all p < 0.01), indicating that IMUGI's calibration advantage is systematic rather than driven by a few influential days.

To assess whether the additional layers of IMUGI provide incremental value beyond simpler alternatives, we estimate two logistic-regression benchmarks and six nested IMUGI variants on the test horizon.

Table 9 shows that the main gain comes from combining the SOHMM and Hawkes signals: M3 improves substantially over either single-signal variant. The later layers do not improve monotonically; M4 yields the best Brier score among the nested IMUGI variants, M5 the highest AUC, and the full specification remains close to the strongest variants on both measures.

The logistic benchmarks further clarify the contribution of the layered architecture. Relative to the simplest logistic benchmark, Full IMUGI improves both AUC and Brier. Relative to the raw same-input logistic benchmark, Full IMUGI improves AUC, whereas LR0 attains the lowest Brier score; in an event-sparse sample, however, a lower Brier score can simply reflect more conservative average probability forecasts rather than a better early-warning model. As the paper's objective is drawdown-onset discrimination with actionable lead time, Full IMUGI remains the preferred specification.

The non-monotonic pattern across M3–M6 is informative rather than necessarily problematic. The largest improvement arises when the SOHMM and Hawkes components are combined, which suggests that these two layers contribute complementary predictive structure. The later additions then redistribute performance across metrics instead of uniformly dominating earlier variants; given a test window containing only three unique drawdown onsets, we do not interpret this as establishing that every additional meta-feature is strictly necessary, and some of the differences among M3–M6 are small relative to the sampling uncertainty.

Taken together, these results indicate that the proposed framework provides better discrimination than standard benchmarks on the full test sample and significantly lower calibrated Brier loss than the external benchmarks. The performance is robust to reasonable variations in the crisis-definition threshold and anticipation window, and the largest single gain arises from combining the SOHMM and Hawkes signals. However performance across the nested variants is not monotonic and the full specification is not uniformly best on every metric; the later layers redistribute performance across discrimination and calibration rather than dominating earlier variants. Within the limits imposed by the small number of significant drawdowns, these results are consistent with the full IMUGI specification extracting incremental predictive value from the same information set.

The framework detected all three onsets: two with actionable anticipatory signals and one confirmed immediately following the shock. Green markers (circles) indicate days where the model exceeded its decision threshold within the nine-day anticipation window prior to each onset; orange markers (diamonds) indicate threshold crossings within five days after the onset. From an applied risk-management perspective, advance warning of up to two weeks and recognition within one week after onset would leave room for timely adjustments to investment strategies. Although three events cannot establish how reliably such lead times recur across future onsets, these results are best read as out-of-sample evidence whose generalisation remains to be tested, rather than as a fully validated operating regime. This performance is consistent with the framework's design objective of balancing sensitivity to early regime change (SOHMM) with event clustering intensity (Q-Hawkes).

Figure 4 presents the model's output across both its raw and calibrated forms alongside the underlying asset price. Crisis probabilities rise sharply during the early accumulation phases of drawdowns rather than exclusively at their deepest points. The 2021 tightening cluster exemplifies regime coherence: both the calibrated and raw series recognised the shared monetary policy shock across all three subsequent anchors, issuing cohesive anticipatory alerts ahead of the unfolding decline. The isotonic calibration compresses the output range while preserving the signal's temporal structure, with the calibrated series issuing cleaner, more decisive threshold crossings relative to the raw output.

IMUGI's core contribution is anticipating overvaluation-driven drawdown onsets at peak rather than identifying them at trough. Network-topological, Laplacian-energy, and recent machine-learning approaches (Tölö, 2020; Zhao et al., 2025; Rao and Rojas, 2025; Ghasemieh and Kashef, 2022) report strong retrospective classification but locate detections near the deepest drawdown point, by which time the institutional hedging window has closed. Detection of all three test-window onsets at or before materialisation is consistent with onset prediction at actionable lead time being feasible, although three events are too few to establish this as a general operating regime.

The meta-model coefficients reveal an interpretable joint-sufficiency structure. The negative loading on raw Hawkes intensity (β₁ = −6.33) combined with the large positive SOHMM–Hawkes interaction (β₅ = +5.50) means jump clustering elevates crisis probability only when concurrent regime instability is detected. Neither signal is sufficient alone, consistent with the regime-dependent jump structure documented by Blanc et al. (2017) and Chen et al. (2024). The ablation reinforces this: the principal gain arises from combining SOHMM and Hawkes signals, with subsequent layers redistributing rather than uniformly improving performance — a pattern consistent with structural rather than memorised signal extraction.

The framework also exhibits a notable near-miss. Crisis probability rose through late October 2023, approached the alert threshold, then fell on 1–2 November 2023 with no accompanying price decline — coinciding with Federal Reserve Chair Powell's press conference, in which he rejected near-term rate cuts and signalled a “higher for longer” regime (Federal Reserve, 2023, pp. 5–16). This is consistent with the framework's indeterministic character: stabilising policy signals can resolve some of the conditions that elevate drawdown probability, so an alert may subside without a subsequent crash. We read this single episode as illustrative rather than causal evidence, but it shows the model retracting a warning in a way that has an economically coherent interpretation.

Two constraints bind the strength of any inferential claim. The first is event sparsity: twelve training onsets and three test events do not support strong claims about hit rates in general, and the test events share identifiable monetary-policy components. The second is mechanistic scope: the LPPL layer is built to detect overvaluation relative to fundamental value, so portability is expected primarily to other asset classes where overvaluation-driven drawdowns are the dominant crisis mechanism — high-multiple growth sectors, cryptocurrencies during bubble episodes, real estate during accumulation phases — rather than to liquidity dislocations, geopolitical shocks, or contagion-driven contractions.

The constituent universe was defined with knowledge of the contemporary AI sector; market-capitalisation weighting structurally attenuates the influence of recently-listed firms in earlier periods, but the index should be read as representing the AI technology sector as currently identified rather than a real-time investable portfolio.

IMUGI integrates three components — regime memory through a Second-Order Hidden Markov Model, self-excitation through a Quadratic Hawkes process, and bubble physics through LPPL-derived features — into a single online probabilistic architecture targeted at the onset of overvaluation-driven drawdowns in AI technology equities. The framework's empirical performance, robustness across event-definition choices, and outperformance of standard survival and machine-learning benchmarks together support the methodological proposition that drawdown onset prediction benefits from joint rather than single-mechanism modelling.

Three extensions follow naturally. Replication on non-US AI equity indices and cross-asset bubbles — cryptocurrencies, real estate during accumulation — would test whether the mechanistic priors generalise beyond NASDAQ-listed technology firms. Integrating external market signals as additional meta-model features may sharpen onset-versus-continuation discrimination within the early-warning window. Extension to other geographies with rapidly accelerating AI sectors — notably the People's Republic of China and the Republic of Korea — offers a natural cross-market test of the framework's calibration. A formal economic-value analysis, with backtested hedging or position-sizing rules, is the most direct path to translating IMUGI's calibrated onset probabilities into measured institutional benefit.

Maksim Kim handled aspects of research execution, from conceptualisation through writing. Seungwook Park provided academic supervision and project administration.

The English in this paper has been refined using Artificial Intelligence tools.

The authors thank 2 reviewers and the editors for helpful comments.

The supplementary material for this article can be found online.