The traditional Power Law model for Bitcoin is limited; it struggles to simultaneously fit historical data points across different eras without piecewise parameter adjustments. Bitcoin's trajectory is more naturally described as a tangent-based hyper-exponential system, driven by absolute supply scarcity.
Serhat Yüksel, Gabriela Oana Olaru, Serkan Eti, Hasan DİNÇER
It is frequently emphasized in the behavioral finance literature that investment decisions cannot be explained solely by economic indicators and rational expectations and that psychological factors also play a significant role in this process. However, the lack of a comparative analysis of the importance of psychological factors influencing investor behavior in the literature and the lack of consensus on which factors are more dominant constitute a fundamental problem. This deficiency leads to significant uncertainties in both theoretical modeling and practical investment strategies, increasing market risks such as irrational price movements, speculative bubbles, and panic selling. In this context, the aim of this study is to determine the relative importance of the fundamental psychological factors influencing investor decisions and, considering these factors, to identify the most appropriate investment alternatives for individuals. This study develops a new integrated decision-making model to answer these research questions. Considering the demographic characteristics of the experts, importance coefficients are calculated using the Euclidean distance-based weighting approach. Criterion weights are then determined using the Entropy method, and the MABAC and MAIRCA methods are applied to rank investment alternatives. Additionally, fractal fuzzy sets based on the Sierpinski triangle are integrated into the proposed model to model uncertainty more effectively. The study's contributions to the literature are highlighted in three dimensions: (1) psychological factors, often overlooked in the literature, are included in the criteria set; (2) expert weights are differentiated based on demographic characteristics rather than assumed to be equal; and (3) expert opinions are modeled more flexibly and precisely using new fractal number-based fuzzy sets. The findings indicate that trust is the most critical psychological factor, followed by loss aversion. In terms of investment alternatives, stocks stand out as the most suitable option, while bonds/deposits and gold are other important alternatives, with cryptocurrencies and real estate ranking next.
The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model complexes on correlated underlyings as a coupled feedback system with matrix gain L and show that scalar monitoring has two blind spots: (i) cycle amplification, since rho(L) >= max_i l_ii for nonnegative coupling, strict under two-way coupling; and (ii) transmitted displacement, which arises already under one-way coupling and is invisible to the receiver's own gain. We give a reduced-form estimator of L requiring only prices and public fund assets -- no signed order flow -- via cross-asset overnight reversals, reporting its measurement-convention sensitivity explicitly. In simulation the spectral radius is recovered with RMSE 0.005 at T=250, a lead-lag confounder yields a 2% false-alarm rate, and in a calibrated blind-spot configuration the scalar monitor reports "safe" and the matrix monitor "unsafe" on 100% of paths. In the 2026 Korean single-stock LETF episode we detect transmission from the SK Hynix complex into Samsung Electronics' closing price (DiD z=-2.82; exact randomization p=0.0055 against 182 control pairs), scaling with the sender's rebalancing capital; conservatively, about 41% of Samsung's closing displacement variance is imported -- invisible to its own "moderate" gain of 0.24. The same estimator returns nulls for the U.S. MSTR-Bitcoin-Coinbase complex, whose capital is comparable but whose closing venue is far deeper. Monitoring should be organized around the (complex x venue) matrix, not around products.
By projecting the 240 E8 root vectors onto a 132 Hz base field and coupling them with the golden‑ratio φ, we can encode the collective meme‑signal state of a cryptocurrency into a discrete spectral pattern. The resulting interference of root‑length harmonics produces a multi‑dimensional volatility waveform that pre‑synchronizes with the ground‑state trading dynamics. When a meme‑triggered sell signal (e.g., PEPE's 5/7 confirmations) is detected, the oscillator re‑shifts phase to amplify the predicted price swing, yielding a ±12 % forecast window. This principle extends MEME SIGNAL analysis and quantum‑breakthrough mining by turning memetic content into a real‑time frequency diagnostic of market flux. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The Holothéic Method is both a mathematical operator and a formalism for extracting predictive information from the second derivative of transition structures in complex fields. Applied here across ten distinct fields simultaneously cryptocurrency markets, geopolitical dynamics, AI adoption, foreign exchange, energy, real estate, and artificial general intelligence the operator identifies ratchet locks: configurations in which a transition has become structurally irreversible. Each prediction is time-stamped, falsifiable, and publicly verifiable within defined deadlines ranging from 72 hours to 12 months. The underlying mechanics are proprietary. This publication establishes intellectual priority as of August 21, 2026, 04:12 CET.
Fernando Henrique Antunes de Araujo, Milena Kojić, Petar Mitić, Kerolly Kedma Felix do Nascimento · 5 authors
This study applies a prespecified dynamic MFDFA workflow across pandemic, geopolitical-conflict, and tariff-policy regimes for ten non-stable, long-history cryptoassets selected ex post from the 23 July 2026 market-cap ranking. The common sample comprises 3155 daily log returns per asset from 2 December 2017 to 22 July 2026; the final endpoint regime includes the U.S.–Iran conflict. The estimator uses q=−10,−8,…,10, linear detrending, 22 scales from 16 to N10, adjacent-secant Legendre transformation, a cubic spectrum peak, and 500-day windows stepped by 21 days plus a terminal endpoint. Full-sample IE=|α0−0.5| ranges from 0.01397 (LINK) to 0.08706 (BNB), and observed width ranges from 0.32625 to 0.74678. The controlled incremental U.S.–Iran endpoint coefficient is −0.02734 (two-way clustered SE 0.02369; p=0.2489), with asset-cluster t(9) interval [−0.08226, 0.02759]. Quantile estimates range from +0.00206 at the 0.10 quantile to −0.04769 at the 0.90 quantile; all five 999-replication asset-cluster bootstrap percentile intervals include zero. Exact rolling sensitivities are negative for the 500/14, 500/30, and 730/30 designs but positive for the 250/21 design, and every small-cluster interval includes zero. Direct spectrum-width contrasts also remain nonsignificant after Holm adjustment. None of ten observed widths survives BH correction in 200 shuffled-return surrogates per asset (2000 fits in total). The results document heterogeneous and specification-sensitive dynamic multifractal patterns, not isolated or causal crisis effects.
When we describe a complicated system by a few coarse measurements, we face one recurring question: are the readings we have now enough to say what it will do next? Sometimes yes; sometimes they look complete but are not, and only pushing the system reveals it. This report turns that question into a checkable procedure. Five inexpensive probes first screen the data — description cost, identifiability, memory duration, change across scale, topological shape — no single probe deciding. We then ask, in order: does the present coarse state beat knowing nothing, and, once known, does history add more. Asking the first matters — history that “no longer helps” can mean the state suffices or that the future is unpredictable, and only the total separates these. Later stages ask whether look-alikes respond differently when pushed. The procedure reports a bottleneck and whether a layer has formed. We calibrate on known-answer cases: a classical system computed end to end (a closed layer, a history-limited case, a case separable only by intervention, and an unpredictable control a naive rule would misread as closed); a charge-to-particle stress test that stops short; and a genuine two-qubit process whose branches are passively identical yet separated by one intervention. We then run real series — carbon dioxide, sunspots, river flow, and equity-index and Bitcoin prices — where next-day returns read as no detected signal while volatility clusters, consistent with what is independently known. Every “no signal” is resource-relative: stamped with the resource R used. The procedure settles only the two ends — a closed layer, or no detected signal — and refuses the process path between; it classifies rather than inventing the next layer’s laws.
The fluctuation characteristics of financial time series have always been one of the research hotspots in the academic community. Generally speaking, financial return series have the characteristics of volatility clustering, fat tails, conditional heteroskedasticity, asymmetric shocks, etc. The above phenomena can be explained from the perspective of dynamic conditional variance by GARCH models and their extensions. This paper first introduces the basic ideas of ARCH and GARCH models, with a focus on the issue of volatility clustering of financial returns. Then, it reviews the relevant research from three aspects: model evolution, application scenarios, and practical value. It also analyzes the role of GARCH-type models in capturing volatility persistence, asymmetric impact, and risk transmission through applications in cryptocurrencies, energy assets, and high-frequency financial data. The study shows that GARCH-type models capture the volatility clustering feature of financial returns well, but there is still room to improve the modeling of extreme risk, the handling of high-dimensional assets, and model interpretability.
The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.
This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) using the Complexity--Entropy Causality Plane (CECP) and directed horizontal visibility graphs (directed HVG) to uncover complex temporal patterns and time-directed structures in the return series. While conventional stylized facts show striking convergence across all assets, structural diagnostics reveal a compelling paradox: cryptocurrencies appear more locally random than the equity benchmark during ordinary periods, yet exhibit significantly stronger directional time-irreversibility around high-visibility return events. The absolute-return results show that large cryptocurrency fluctuations tend to begin abruptly and remain elevated afterward. Separate analyses of positive returns and negative-return magnitudes show that this pattern is shared across cryptocurrencies on the upside but varies across assets on the downside. We conclude that statistical maturity is only skin-deep; the underlying dynamical processes of mature cryptocurrencies remain fundamentally distinct from traditional benchmarks.