Wavelet Transform
Time-frequency multi-scale price decomposition
Overview
Wavelet Transform decomposes price series into time-frequency components simultaneously, revealing cyclical patterns across multiple scales (timeframes) at once. Unlike FFT which loses timing info, wavelets preserve when frequencies occur. Morlet or Mexican Hat wavelets stretch/compress across scales = continuum frequency analysis. Reveals dominant market cycles (4-day, 10-day, 25-day, etc.) with timing precision = superior to fixed-period oscillators.
Wavelet power spectrum shows intensity of each frequency at each time point. High power = dominant cycle active. Watch for power concentration at 2-3 specific periods = mechanical trading signal. When dominant cycle shifts abruptly (cycle death), regime change = trend/consolidation transition. Requires statistical signal processing knowledge but delivers unique edge unavailable from standard indicators.
Professional quantitative traders use wavelets for cycle timing, regime detection, and optimal entry/exit windows. More sophisticated than moving averages; far superior to fixed-period oscillators for adaptive trading.
Formula
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
| Wavelet Type | Selection | Morlet | Morlet for sharp peaks, Mexican Hat for broad cycles |
| Frequency Range | Period Bars | 4-128 bars | Min/max cycle lengths to analyze |
| Power Threshold | Percent | 75th percentile | Highlight only significant power concentrations |
Common Use Cases
1. Dominant Cycle Detection
Identify current market cycle (4/10/25-day periods). High concentration = mechanical signal for period-matching trades.
2. Regime Change Detection
Power shifts between scales = cycle death/birth. Sudden change = regime switch from trending to choppy.
3. Entry/Exit Timing
Peak power = optimal entry window within dominant cycle. Trough = optimal exit. Mechanical timing.
4. Confluence Across Cycles
When 2+ dominant cycles align in phase = strongest signals. Multi-scale power concentration.
Advantages & Limitations
✓ Advantages
- Multi-Scale Analysis: Simultaneous view of all frequencies; reveals relationships FFT misses.
- Time-Frequency Precision: Know WHEN frequencies are active; superior to Fourier.
- Adaptive Cycles: Markets naturally cyclical; wavelets reveal true dominant period.
- Quantitative Edge: Rare edge; most traders unaware; automation possible.
! Limitations
- Computationally Intensive: CWT requires O(n²) calculations; slow on long histories.
- Interpretation Difficulty: Power maps complex to read; requires DSP knowledge.
- Edge Artifacts: Boundary effects at chart edges reduce reliability on recent bars.
- Lookback Dependency: Cycle detection lags; must wait ~2 periods for confirmation.
Tips & Best Practices
📊 Focus on Concentration
Watch power map for tight clustering at 1-2 periods. Broad/scattered = no dominant cycle = avoid trading.
⚡ Ignore Edge Artifacts
Recent bars (last ~10% of lookback) unreliable due to boundary effects. Trade only stable cycles from older bars.
🎯 Use on Daily+ Charts
Wavelets work daily/weekly; intraday cycles too noisy. 4-128 bar range = 4-day to 25-week cycles on daily.
⚠️ Confirm with Price
Wavelet signal not standalone. Confirm cycle prediction with price structure (FVG, Order Block).
Example Strategy
1. Scan Power Map
Daily chart: plot wavelet power (4-128 bars). Identify tight concentration = dominant cycle present.
2. Measure Cycle Period
When power concentrates at specific period (e.g., 10 bars), note it. Market currently cycling at that frequency.
3. Time Wave Projection
Assume price oscillates at detected period. Project next ~(period/2) bars = expected trend reversal. Plan entry.
4. Exit at Cycle Peak/Trough
When price reaches projected peak/trough (cycle peak), exit. Stop loss beyond prior cycle extreme point.