Identifying and Quantifying Financial Bubbles with the Hyped Log-Periodic Power Law Model

TL;DR

This work develops the Hyped Log-Periodic Power Law (HLPPL) model to identify and quantify financial bubbles and negative bubbles by marrying the LPPL framework with behavioral signals. It introduces a Bubble Score computed from LPPL residuals, a Sentiment Score from FinBERT, and a Hype Index to capture media attention, all integrated within a Dual-Stream Transformer that forecasts short-horizon bubble intensity. Key contributions include (i) a bidirectional detection framework that handles both overpricing and underpricing, (ii) empirical evidence of robust backtested performance (average annualized return $34.13\%$) and sector-wide generalization, and (iii) a machine-learning–enhanced trading strategy that substantially improves returns versus a rules-based baseline, with notable gains for HOUS. The approach advances bubble research by enabling forward-looking, signal-rich trading decisions that integrate technical dynamics with market psychology, offering practical implications for risk management and asset allocation in real time. Future work will broaden the scope beyond real estate, refine horizons, and incorporate additional macro-financial indicators to further enhance real-time monitoring and decision-making.

Abstract

We propose a novel model, the Hyped Log-Periodic Power Law Model (HLPPL), to the problem of quantifying and detecting financial bubbles, an ever-fascinating one for academics and practitioners alike. Bubble labels are generated using a Log-Periodic Power Law (LPPL) model, sentiment scores, and a hype index we introduced in previous research on NLP forecasting of stock return volatility. Using these tools, a dual-stream transformer model is trained with market data and machine learning methods, resulting in a time series of confidence scores as a Bubble Score. A distinctive feature of our framework is that it captures phases of extreme overpricing and underpricing within a unified structure. We achieve an average yield of 34.13 percentage annualized return when backtesting U.S. equities during the period 2018 to 2024, while the approach exhibits a remarkable generalization ability across industry sectors. Its conservative bias in predicting bubble periods minimizes false positives, a feature which is especially beneficial for market signaling and decision-making. Overall, this approach utilizes both theoretical and empirical advances for real-time positive and negative bubble identification and measurement with HLPPL signals.

Figures (12)

• Figure 1: LPPL residual-only detection for HOUS. The black line shows log prices and the blue dashed curve the LPPL fit. Green (red) bands denote intervals where the observed series is materially above (below) the theoretical path. A clear local peak is detected in mid-2023, followed by a prolonged oversold phase into late-2023; however, short and noisy swings can still trigger event windows under the residual-only approach.
• Figure 2: HLPPL (BubbleScore) detection for HOUS. By augmenting residual information with a Hype index and text Sentiment, and enforcing minimum-duration and threshold rules, spurious short-lived windows are filtered out and the alternating bubble/negative-bubble phases over 2022–2024 are delineated more crisply (including the mid-2023 top and the late-2023 to early-2024 rebound).
• Figure 3: Signal comparison: BubbleScore (with Hype & Sentiment) vs. residual-only. The two signals agree on major turning points, but HLPPL is smoother around decision thresholds (e.g., $\pm 0.4$), produces fewer flips during choppy regimes, and down-weights moves that lack media attention or textual-emotion corroboration—reducing false positives/negatives and improving tradeability.
• Figure 4: Daily BubbleScore time series for HOUS with threshold bands and event shading. The sequence of up-crossings in mid-2023, subsequent down-crossings in late-2023, and re-entries above the upper band in early-2024 illustrates the regime rhythm under a unified "behavioral + technical" lens. Peak markers assist rule-based entries, scaling, and profit-taking.
• Figure 5: LPPL residual-only detection for AMTX. The black line shows the log price and the blue dashed curve the LPPL fit. Green (red) shading marks intervals where prices lie materially above (below) the theoretical path. Distinct positive-bubble episodes appear in 2021–2022, while early-2018 and mid-2020 exhibit pronounced negative-bubble behavior.