Educational Resources
Cycle Analysis Guides
Learn about market structure, cycle detection methods, and the principles behind the Fractal Cycles framework. Structure over narrative.
Fundamentals
Understanding Market Cycles
Why markets exhibit recurring patterns and how to identify them through structural analysis.
Multi-Timeframe Cycle Nesting
How cycles nest within cycles and why timeframe alignment matters.
How to Detect Market Cycles
A beginner-friendly guide to finding hidden cyclical patterns using spectral analysis and statistical validation.
Why Cycles Beat Indicators
Understanding why structural cycle analysis outperforms traditional indicator-based approaches.
Why Narrative-Based Market Analysis Fails
When the loudest voices in finance offer no evidence, what are they actually saying? A framework for distinguishing market commentary from market structure.
Cycle Analysis vs Technical Analysis
Quantitative structure vs pattern recognition: where each approach works best and how to combine them.
The Four Phases of a Market Cycle
How Accumulation, Markup, Distribution, and Markdown map onto Hurst regime signatures and spectral phase readings.
Cyclic Analysis: A Complete Guide to Market Cycles
What cyclic analysis is, how it works, and how traders use it to identify recurring patterns in price data.
Stock Market Cycles Explained: How to Spot Them First
The science behind stock market cycles, what drives them, how to detect them, and what they mean for your portfolio.
The Presidential Cycle and the Stock Market
How the four-year presidential election cycle affects stock market returns, what the data shows and what it means for investors.
What Is Mean Reversion in Trading? The Complete Explanation
Mean reversion explained from first principles, why prices return to averages, when the theory holds, and when it breaks down.
Stock Market Cycles History: Major Cycles from 1900 to Today
A data-driven look at historical stock market cycles, the major patterns, their durations, and what spectral analysis reveals about them.
Core Methods
The Hurst Exponent Explained
How to distinguish trending markets from ranging markets using statistical persistence measures.
The Goertzel Algorithm for Cycle Detection
How spectral analysis extracts dominant frequencies from market data.
Bartels Significance Testing
Separating genuine cycles from random noise using statistical validation.
Detrending Methods Compared
Comparing different approaches to removing trend before cycle analysis.
Cycle Detection Methods Compared
FFT, Goertzel, and wavelets: when to use each cycle detection approach.
Spectral Analysis for Trading
How frequency-domain methods reveal hidden structure in market data that time-domain tools miss.
Hurst Deep Dive
Hurst Exponent in Python
Complete implementation guide for calculating R/S analysis programmatically.
Hurst Exponent in Excel
Step-by-step spreadsheet approach for traders who prefer no-code solutions.
Rolling Hurst Exponent
Track regime changes dynamically with rolling window Hurst analysis.
Hurst Exponent Interpretation
What specific H values mean and how to act on them in practice.
Hurst Exponent Across Timeframes
Why Hurst values differ across timeframes and what it means.
Cycle Analysis
Dominant Cycle Period
How to identify which cycle length matters most in any market.
Multiple Cycle Analysis
How overlapping cycles interact, interfere, and create complex patterns.
Cycle Phase Interpretation
Understanding where you are within a cycle and what it implies.
Cycle Phase Determination
Methods for calculating your current position within detected cycles.
Cycle Amplitude Dynamics
What causes cycles to strengthen or weaken over time.
Composite Wave Construction
How to combine multiple cycles into a single projection wave.
Cycle Length vs Volatility
The relationship between cycle period and price movement magnitude.
Spectral Analysis for Non-Stationary Data
Handling real market data that violates stationarity assumptions.
Composite Cycle Wave Projection
How combining validated cycles into a forward projection creates a structural roadmap.
How Long Do Market Cycles Last?
Typical durations by cycle type, mapping J.M. Hurst's nominal hierarchy to detected periodicities across asset classes.
Hurst Cycles Explained: The Complete Guide
J.M. Hurst's cyclic model for financial markets, the principles, the nominal model, and how modern tools apply it.
Stock Market Cycle Analysis: How to Detect and Trade Cycles
A practical guide to analyzing stock market cycles using spectral analysis, Hurst exponent, and Bartels significance testing.
Cyclical Market Analysis: Finding Patterns in Price Data
How cyclical market analysis uses spectral methods and statistical testing to reveal hidden patterns in financial time series.
Cyclical Analysis Explained: A Practical Introduction
What cyclical analysis is, the four methodological steps (detrend, spectral decomposition, Bartels testing, Hurst regime filter), and how to apply it to real markets.
Hurst Cycle Software and Tools: A Practical Comparison
Comparing Hurst cycle analysis tools, from manual methods to automated platforms, and what to look for in cycle detection software.
The 84-Week Cycle: Why Hurst's 18-Month Nominal Keeps Showing Up
Spectral analysis detects the same 84-week cycle across the Dollar Index, S&P 500, Bitcoin, Gold, and crude oil, confirming Hurst's 18-month nominal model.
Statistical Validation
The Bartels Test Explained
Why most detected cycles are noise and how Bartels testing filters them.
Statistical Significance in Cycles
What p-value threshold makes a cycle tradeable.
Overfitting in Cycle Detection
How to prevent curve-fitting to historical noise.
Cycle Persistence Testing
Assessing whether detected cycles are likely to repeat.
Is Cycle Analysis Reliable?
The statistical evidence: cross-asset Bartels significance, multi-decade persistence data, and honest limitations.
Market Regimes
Why Compression Precedes Expansion
The structural relationship between low-volatility compression and subsequent price expansion.
Market Regime Detection
Objective methods to classify trending, ranging, and transitional states.
Volatility Cycles
Why volatility clusters and how to detect its cyclical patterns.
Mean Reversion Conditions
What market conditions make mean-reversion strategies viable.
Trend Following in Different Regimes
How trend systems should adapt to structural conditions.
Regime Transition Signals
Early warning signals that precede regime shifts.
How to Know If a Market Is Trending or Ranging
Use data, not guesswork, to determine whether a stock is trending or mean-reverting, and which strategy to apply.
How to Identify Market Trends Before They End
Practical methods for detecting stock market trends, from moving averages to Hurst exponent regime detection.
Practical Application
Swing Trading Within Cycle Structure
How to identify swing opportunities using dominant cycle phases.
Intraday Cycle Awareness
How intraday patterns express underlying multi-timeframe structure.
Position Sizing Based on Hurst Regime
Adapting position size based on market regime characteristics.
Stop Loss Placement Using Cycle Structure
Structural approach to stop loss placement based on cycle phase.
Entry Timing Within Cycle Phases
Identifying favorable entry windows within cycle structure.
Exit Timing and Cycle Phase Targets
Structural frameworks for identifying potential exit zones.
Integrating Cycles with Price Action
Combining cycle awareness with price action interpretation.
Regime-Based Asset Allocation
How regime identification informs allocation decisions.
When Cycles Fail: Structural Breakdown Analysis
Recognizing and responding when cycle projections break down.
The Limits of Backtesting in Nonlinear Market Systems
Why historical testing of cycle-based approaches faces fundamental challenges.
Cycle-Aware Trading Strategy
How to use cycle analysis as a structural filter that improves existing trading strategies.
Cycle Trading: The Complete Guide
From detecting cycles with spectral analysis to building a cycle-aware strategy, the full discipline in one place.
How to Apply Hurst Cycle Analysis to Any Market
A practical, step-by-step walkthrough of performing Hurst cycle analysis on stocks, crypto, and commodities.
Advanced Hurst
The History of the Hurst Exponent
From the Nile to financial markets: how Hurst discovered persistence.
R/S Analysis vs Detrended Fluctuation Analysis
Comparing two leading methods for estimating the Hurst exponent.
The Hurst Exponent and Market Efficiency
What Hurst tells us about the efficient market hypothesis.
Confidence Intervals for Hurst Estimates
Understanding and calculating uncertainty in Hurst measurements.
Hurst Exponent vs Variance Ratio Tests
Two approaches to measuring persistence compared.
Hurst Exponent vs Autocorrelation
Short-range vs long-range dependence and why the distinction matters.
Fractal Dimension and the Hurst Exponent
The geometric meaning of persistence and the D = 2 - H relationship.
Hurst Exponent in the Context of Efficient Markets
What range of Hurst values is consistent with market efficiency.
Hurst Exponent: Anomalies and Limitations
Edge cases, biases, and common pitfalls in Hurst estimation.
Hurst Patterns Across Asset Classes
How different markets exhibit different persistence characteristics.
Trading Strategies
Mean Reversion Trading Strategy: A Data-Driven Guide
How mean reversion works, which indicators to use, and how to confirm a mean-reverting regime with the Hurst exponent.
Trend Following Strategy: How to Ride Trends with Confidence
How trend following works, the indicators that matter, and how to confirm a trending regime before committing capital.
Mean Reversion Indicators: Which Ones Actually Work
A data-driven comparison of Bollinger Bands, RSI, CCI, Z-score, and Hurst exponent for identifying mean reversion opportunities.
Crypto Cycles
Bitcoin Halving Cycle: What Past Halvings Reveal About Price Behavior
Examining all four Bitcoin halvings, what the price data shows about post-halving rallies, where the narrative oversimplifies, and how cycle analysis adds depth.
How to Analyze Bitcoin's Cycle Position Using Spectral Methods
A framework for determining where Bitcoin sits in its multi-year cycle structure using spectral analysis, regime detection, and halving-cycle comparison.
How to Find the Dominant Cycle in Any Cryptocurrency
A step-by-step guide to detecting statistically significant cycles in Bitcoin, Ethereum, and altcoins using spectral analysis and the Bartels test.
Market Timing
How to Predict Stock Market Movements: What the Data Actually Shows
Nobody can predict exact prices. But cycle analysis, regime detection, and statistical validation offer something better than guessing.
Stock Market Cycles Forecast 2026: What Cycle Analysis Reveals
Where does the S&P 500 sit in its cyclical structure heading into 2026? Presidential cycle, spectral analysis, and regime detection provide context.
These guides describe observable market structure through the Fractal Cycles framework. They do not provide forecasts, recommendations, or trading instructions.Learn about our methodology
Apply these concepts to real data
See how cycle analysis works in practice with our interactive tools.