Free lesson · Technical analysis

Momentum indicators, oscillators and divergence

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• Rate of change compares the current price with a prior price. It measures past movement, not a future return.
• RSI compares smoothed gains and losses. MACD compares fast and slow EMAs; stochastic %K places the close within a trailing range. Read the indicator equations and initialization rules.
• Overbought means a high reading under an indicator’s definition. A strong trend can remain overbought; it is not an automatic short signal.
• Bullish regular divergence can mean a lower confirmed price low with a higher indicator low. Bearish regular divergence mirrors this at highs.
• Hidden divergence uses different high/low comparisons and is commonly interpreted as continuation. Define its exact geometry instead of reusing a generic label.
• Align price and indicator pivots by an explicit tolerance. Both must be confirmed before the divergence exists in the decision record.
• Compare divergence against momentum alone and matched volatility/trend events. Many indicator settings and pivot pairings create multiple-testing risk.

Use the rule

• Fix the definition, units and information timestamp.
• Compute the example and inspect the graph.
• Compare with a simple baseline on untouched periods after costs.

Before moving on

Write the exact rule, its availability time, an invalidation condition and a fair out-of-sample test.

Research checkpoint · reviewed 12 September 2026

• Status: unreviewed arXiv preprint; empirical-design and limitations sections reviewed. Its own disclosure says no untouched holdout remains.
• Scope: selected trend, oscillator, volume, candle and calendar rules. Examples include Russell 3000 volume data for 2007–2025 and a S&P 500 momentum comparison for 2000–2026; several other rows report only “full sample.”
• The reported bootstrap resamples previously examined data. Cost assumptions are parameterized, and universes differ across rule families. These limits prevent treating the paper as a clean prospective comparison.
• Use the methodological questions—material effect size, costs and uncertainty—to design a fresh test. Its scope excludes channel breakouts and wider chart formations; it cannot settle all topics in this module.

Darmanin · Retail Trader’s Ruin (July 2026 preprint) ↗

def momentum_oscillator(close,lagged_close,low,high):
    if lagged_close<=0 or high<=low or not low<=close<=high: raise ValueError("Valid positive lag and nonzero range required")
    return close/lagged_close-1,100*(close-low)/(high-low)

print(momentum_oscillator(105,100,95,110))