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Long-term price models and cycles

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Long-term price-modeling and cycle-analysis frameworks for Bitcoin. The area divides cleanly into two clusters. Long-term trajectory models capture Bitcoin's secular price path on multi-year-to-multi-decade horizons — the Power Law as the current consensus framework, Stock-to-flow as the prior framework retained for its hardness-as-measure dimension, plus logarithmic regression, Metcalfe-style network-value models, the Lindy effect, and adoption-curve frameworks. Cyclical and macro-regime models capture the oscillatory and regime-driven structure superimposed on the trend — the four-year halving cycle, the Perrenod-Santostasi log-periodic wave model, the global-liquidity correlation framework, and the ISM/PMI cyclical framework. The two clusters operate at different scales: the trajectory models address where Bitcoin is going on a 10-year horizon; the cyclical and macro models address where it is now within an oscillation around that trend. Together they form the quantitative scaffolding for long-horizon allocation, cycle-aware positioning, and macro-correlation analysis. Principal anchors are Santostasi and Perrenod (Power Law and the log-periodic framework — both members of the Scientific Bitcoin Institute), Plan B (engaged critically on S2F), and macro-correlation operationalizers such as sminston_with.

How to use this sub-MOC

The notes here are arranged in three ways simultaneously:

  1. By cluster — trajectory vs. cyclical/macro, reflecting the two distinct conceptual scales of modeling
  2. By suggested reading order — for someone working through the area systematically
  3. By function — distinguishing framework notes, comparison notes, and critique notes

Each note is a deep treatment that can be read on its own. The clustering here is for navigation, not redundant summary.

The intellectual structure

The price-models area operates on a two-scale framework:

Scale 1 — The long-term trajectory. What is the structural path Bitcoin’s price is on across many years? The Power Law model and its predecessors and adjuncts (Stock-to-flow, log-regression, Metcalfe-style network-value models, Lindy, adoption curves) address this. The trajectory models tell you where Bitcoin is likely to be in 5, 10, or 20 years given continued adoption — they are essentially secular frameworks.

Scale 2 — Cyclical and macro-regime structure. What oscillations and regime dynamics ride on top of the secular trend? Four-year halving cycles, the Perrenod-Santostasi log-periodic wave model (which extends Power Law into the cyclical domain via discrete scale invariance), the global-liquidity correlation framework (Bitcoin tracks central-bank-driven global liquidity at ~10-12 week leads/lags), and the ISM/PMI cyclical framework (Bitcoin’s price-cycle positioning relative to the manufacturing-cycle leading indicator) address this. These models tell you where Bitcoin is now within an oscillation around the trend.

The framework synthesis: trajectory + cycle = a coherent quantitative position on Bitcoin’s near-term and long-term price behavior. Allocation decisions should engage both. Long-horizon allocation rests primarily on the trajectory framework; cycle-aware positioning rests primarily on the cyclical/macro framework.

A third genus, treated outside this sub-MOC, is the real-terms ceiling frame — frameworks that estimate Bitcoin’s full-potential valuation in today’s dollars without committing to a specific time-path. Bitcoin’s addressable market (Economics) treats this; the framework is complementary to the trajectory frames here, not in competition with them. The Power Law tells you the path; the addressable-market frame tells you the asymptote.

This area is theoretical-argumentative in voice (parallel to Economics and Culture-philosophy), not operational. Each note presents a model, its mechanism, its empirical fit, its predictions, and the steelmanned counter-arguments.

Long-term trajectory models

These notes treat the secular price path. Each is structured as: what the model claims, the underlying mechanism, empirical fit, predictions, and counter-arguments.

  • The Power Law model — Santostasi and Perrenod’s framework: with . Price as power-law function of time since genesis, mechanism grounded in network-effects-driven adoption (Metcalfe-style). The current consensus long-term framework. Cross-listed in Economics because the underlying mechanism is load-bearing for the Austrian-Bitcoin synthesis.
  • Stock-to-flow model — Ammous’s hardness framework (surviving) and Plan B’s price model (broken post-2021). The critique content from the formerly-separate “Critiques of stock-to-flow” note is integrated into this note’s counter-arguments section. Cross-listed in Economics.
  • Logarithmic regression and rainbow charts — The pre-Power-Law family of long-term frameworks. Trolololo’s log-regression and the rainbow-chart visualization. Treated as Power-Law-precursor frameworks with weaker theoretical grounding but historical importance.
  • Metcalfe’s Law applied to Bitcoin — The network-value framework. applied to Bitcoin’s active-address count; Tim Peterson’s quantitative work; relation to Power Law as underlying mechanism.
  • Lindy effect and Bitcoin — The Lindy framework: technologies that have survived years are expected to survive more. Taleb’s formalization; Lindy as Bitcoin-survival case rather than price model directly.
  • Adoption curves — Rogers’ diffusion-of-innovations framework, S-curve adoption (Weibull CDF as Perrenod’s preferred form), where Bitcoin currently sits in its adoption curve. Distinct from but complementary to Power Law.
  • Diminishing returns thesis — The cycle-over-cycle declining-return-amplitude framework. Naturally embedded in Power Law; treated explicitly here. Implications for cycle-top expectations and long-horizon allocation.

These seven trajectory models form a connected set. Power Law is the centerpiece; the others either feed into it (Metcalfe, Adoption curves), precede it (Log-regression), complement it (Lindy, Diminishing returns), or are engaged critically (Stock-to-flow as price model).

Cyclical and macro-regime models

These notes treat the oscillatory and regime-driven structure that rides on top of the secular trend.

  • Four-year halving cycles — The halving-anchored cycle framework. The 2011, 2013, 2017, 2021, and 2024-2025 cycles compared; whether halvings drive cycles causally or are merely time markers; the Perrenod-log-periodic critique of halving-as-master-cycle (with the 2021 peak treated as a harmonic rather than a fundamental).
  • Log-periodic cycles and the Perrenod-Santostasi wave model — Discrete scale invariance superimposed on the Power Law’s continuous scale invariance. Sinusoidal-in-log-time oscillations explaining ~74% of the residual variance around the Power Law trend. Fundamental cycles when Bitcoin’s age doubles (λ ≈ 2.01); harmonics; the coupling constant . Published through the Scientific Bitcoin Institute.
  • Bitcoin and global liquidity — The Howell/CrossBorder-Capital framework. Bitcoin’s mid-horizon price correlates with global central-bank liquidity (M2 plus reserve dynamics) at ~10-12 week leads/lags. Operationalized by sminston_with and others; Alden engages it within her broader macro framework.
  • Bitcoin and the ISM PMI cycle — The manufacturing-cycle leading-indicator framework. ISM Manufacturing PMI as a forward-looking signal for risk-asset and Bitcoin cyclical positioning. Less canonical than global liquidity but increasingly cited by macro-aware Bitcoin analysts.

The four cyclical/macro notes operate at different scales: halving cycles on a four-year-ish anchor; log-periodic at multiple harmonics; global liquidity at ~10-12 week lead/lag; ISM/PMI at quarterly business-cycle frequency. Each adds information the others don’t capture.

Analytical voices anchoring this area

The area has a dense thinker-page foundation:

Power Law framework

Stock-to-flow framework (engaged critically)

  • Plan B — Pseudonymous Dutch institutional investor; originator of the S2F price model. Engaged charitably but the framework is treated as superseded for price prediction.

Global-liquidity and macro-correlation framework

  • Michael Howell — Founder and CEO of CrossBorder Capital (London); originator of the Global Liquidity Index (GLI) and the canonical institutional developer of the global-liquidity framework. Capital Wars: The Rise of Global Liquidity (2020) is the book-length statement. The macro anchor for Bitcoin and global liquidity.
  • sminston_with — YouTube-based macro-correlation analyst; operationalizes Howell’s global-liquidity framework and the ISM/PMI framework for Bitcoin. Treated as a popularizer/operationalizer rather than originator.

Adjacent voices cited from this area

  • Lyn Alden — Engineer-macroeconomist; uses global-liquidity framing within a broader fiscal-dominance macro framework. Home in Economics; cited in this area for the macro-correlation models.
  • Saifedean Ammous — The hardness-as-measure dimension of Stock-to-flow; home in Economics; cited in the S2F note.
  • James Check — On-chain analyst; cycle-positioning work at shorter timescales than the trajectory models. Home in on-chain; cited where on-chain analytics interact with price models.
  • Ryan - On-Chain Mind — On-chain analyst; cycle-positioning at shorter timescales. Home in on-chain.

Key connections to other areas

Price models are not a self-contained domain. The area is dense with cross-references:

To Economics and monetary theory

  • The Power Law and Stock-to-flow notes are cross-listed under Economics because their mechanisms (network adoption, monetary hardness) are load-bearing for the Austrian-Bitcoin synthesis.
  • Network effects and Metcalfe’s Law (home: economics) is the underlying network-economics framework Power Law extends.
  • Monetization S-curve (home: economics) is the adoption-side framework Power Law operationalizes mathematically.
  • Hard money vs fiat money (home: economics) is the hardness precondition for the Power Law’s adoption mechanism.
  • Origins of money (home: economics) — Mengerian salability framework underlying the network-effects mechanism.

To On-chain analytics

  • The cyclical models operate at multi-month to multi-year scales; on-chain frameworks operate at intra-cycle scales. The two are complementary, not competing.
  • James Check and Ryan - On-Chain Mind anchor on-chain cycle analysis; this area provides the longer-horizon scaffolding their work sits within.

To Investing and markets

  • Portfolio approaches to Bitcoin (home: investing) is the practical destination of this area’s frameworks. Trajectory models inform long-horizon allocation; cyclical models inform within-cycle positioning.
  • DCA, lump-sum, and cycle-aware allocation decisions all rest implicitly on a position about which trajectory and cyclical frameworks are credible.

To Mining

  • The halving - Mechanism (home: economics, but the technical mechanism is in mining) is the supply-schedule event the halving-cycle framework anchors on.
  • Hashrate dynamics relate to Power Law’s intrinsic-driver formulation (Santostasi treats hashrate and address count as the underlying drivers of the price power law).

What this area doesn’t cover

To set expectations for what isn’t here:

  • Short-term price prediction. Trading-frequency price modeling (daily, weekly, intraday) is not addressed. The shortest timescale this area engages is monthly-to-quarterly (global liquidity, ISM/PMI).
  • Pure technical analysis. Chart-pattern frameworks (Elliott Wave, head-and-shoulders, Wyckoff) are not treated as serious price models in this section. The area focuses on mechanism-grounded quantitative frameworks.
  • Altcoin price modeling. Altcoin price models, “alt season” cycle frameworks, and BTC dominance as a trading signal are out of scope.
  • Specific exchange-flow or on-chain metric forecasting. This is the on-chain analytics area’s domain.
  • Macroeconomic forecasting independent of Bitcoin. The global-liquidity and ISM/PMI frameworks are engaged for their connection to Bitcoin price; the underlying macro-forecasting question is for Alden’s area and the broader investing-and-markets area.

The boundary with on-chain analytics is the most porous; cycle-positioning work bridges both areas.

Open questions in this area

  • When does the Power Law break down? A pure power law goes to infinity; Bitcoin’s appreciation must eventually slow. At what fraction of global monetary wealth does the framework fail, and what replaces it?
  • Is the four-year halving cycle the master cycle or a secondary harmonic? The Perrenod log-periodic framework argues the 2021 peak was a harmonic, not a fundamental. The question affects how to interpret 2024-2025 and beyond.
  • How tight is the global-liquidity correlation? Howell’s framework gives a specific lead-lag; the question is whether the relationship is structural or coincidental, and whether it survives a major-central-bank policy regime change.
  • Does the Power Law exponent evolve? Some analyses suggest k has shifted slightly across Bitcoin’s history. If so, the framework’s predictive power depends on which exponent is current.
  • How does fiscal dominance (Alden) interact with the Power Law mechanism? Structural acceleration in monetary debasement could shift the adoption dynamics the Power Law captures.
  • What is the appropriate institutional response when both trajectory frameworks (S2F, Power Law) and cyclical frameworks (4-year cycle) are eventually shown to be incomplete? The model-succession problem is unresolved.
  • Should ISM/PMI be treated as a real Bitcoin price-cycle framework or as a secondary correlate of global liquidity? The two macro frameworks may be redundant or complementary.

Canonical sources across the area

Primary sources (built or to be built)

  • Giovanni Santostasi, “The Bitcoin Power Law Theory” (Medium, canonical exposition) — see Giovanni Santostasi
  • Stephen Perrenod, Substack at stephenperrenod.substack.com — see Stephen Perrenod
  • Santostasi and Perrenod, “A Mechanistic Derivation of the Bitcoin Price Power Law: Network Adoption Dynamics and Generalised Metcalfe Scaling” — Scientific Bitcoin Institute paper
  • Plan B, original S2F articles (2019, 2020) — engaged critically; see Plan B and Stock-to-flow model
  • Michael Howell — Capital Wars: The Rise of Global Liquidity (2020) and ongoing CrossBorder Capital research; the canonical global-liquidity statement engaged in Bitcoin and global liquidity

Adjacent canonical sources from other areas

  • The Bitcoin Standard (Saifedean Ammous) — hardness framework; cited from Stock-to-flow model
  • Broken Money (Lyn Alden) — macro framework intersecting global-liquidity model
  • The Bullish Case for Bitcoin (Vijay Boyapati) — adoption-curve framework

Background mathematical and network-economics literature

  • Bob Metcalfe, original Metcalfe’s Law writings (1980)
  • David Reed, Reed’s Law
  • Everett Rogers, Diffusion of Innovations
  • Didier Sornette, log-periodic power law work in financial markets (the broader literature from which the Perrenod-Santostasi log-periodic framework draws)

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