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Wavelet Analysis

A diagnostic multi-scale decomposition study for visualizing how price action decomposes across different frequency bands. Ideal for research, understanding market structure, and developing custom strategies.

Overview​

The Wavelet Analysis study shows you the "internals" of wavelet decomposition:

  • Detail Bands (D1-D7): High to low frequency components
  • Approximation (A_J): The underlying trend
  • Optional Denoising: See the effect of noise removal
  • Signed RMS View: Energy direction per level

This study is for research and analysis — it helps you understand which frequency bands contain the information you care about.

How It Works​

Using MODWT (Maximal Overlap Discrete Wavelet Transform) with symmetric boundaries:

  1. Input: Close prices (or selected price source)
  2. Decomposition: Split into J detail levels + 1 approximation
  3. Visualization: Each level plotted in separate panel or overlaid

Frequency Interpretation​

LevelCapturesTypical Timeframe
D1Highest frequency noise2-4 bars
D2Short-term fluctuations4-8 bars
D3Intraday swings8-16 bars
D4Daily patterns16-32 bars
D5Weekly patterns32-64 bars
D6-D7Longer cycles64+ bars
A_JTrendLongest scale

Display Options​

Multi-Panel View​

Each detail level in its own panel:

  • D1 at top (fastest)
  • D7/A_J at bottom (slowest)
  • Clear separation of frequency bands

Signed RMS View​

Instead of raw coefficients, show directional energy:

  • Positive RMS → bullish energy at that scale
  • Negative RMS → bearish energy at that scale
  • Easier to read for trading decisions

Overlay Mode​

All levels on one panel with different colors:

  • Useful for seeing phase relationships
  • Can be visually busy with many levels

Settings​

Wavelet Transform​

SettingDefaultDescription
Wavelet TypeDB4Wavelet family
Decomposition Levels5Number of detail bands (D1 to D_J)
BoundariesSymmetricBoundary handling (symmetric recommended)

Denoising​

SettingDefaultDescription
Apply DenoisingfalseEnable threshold-based noise removal
Threshold MethodBayesBayesShrink or Universal
Shrinkage TypeSoftSoft or Hard thresholding

Display​

SettingDefaultDescription
View ModeMulti-PanelMulti-Panel, Overlay, or Signed RMS
Show ApproximationtrueInclude A_J in display
Show DetailsD1-D5Which detail levels to show

Use Cases​

Finding the Right Decomposition Level​

Before using SWT Trend + Momentum, use Wavelet Analysis to determine:

  1. Which levels contain mostly noise (typically D1-D2)
  2. Which levels contain your trading signals
  3. Optimal decomposition depth for your timeframe

Understanding Market Regimes​

Different market conditions show different energy patterns:

  • Trending: Energy concentrated in lower frequencies (D4+, A_J)
  • Ranging: Energy spread across mid-frequencies (D2-D4)
  • Volatile: Spikes in high frequencies (D1-D2)

Developing Custom Indicators​

Use the decomposition to build custom signals:

  • Energy ratio between scales
  • Cross-scale divergence
  • Level-specific momentum

Validating Denoising Settings​

Toggle denoising on/off to see:

  • What gets removed as "noise"
  • Whether important signals are preserved
  • Optimal threshold settings for your data

Interpreting the Output​

Raw Coefficients​

  • Oscillate around zero
  • Magnitude = energy at that scale
  • Sign = direction of movement

Signed RMS​

  • Smoother visualization
  • Positive = bullish pressure
  • Negative = bearish pressure
  • Larger magnitude = stronger conviction

Cross-Scale Patterns​

Look for alignment across scales:

  • All levels positive: Strong bullish alignment
  • All levels negative: Strong bearish alignment
  • Mixed signals: Consolidation or reversal zone

Troubleshooting​

Too Many Bars Required​

  • Reduce Decomposition Levels
  • Use shorter lookback period

Noisy Display​

  • Enable Apply Denoising
  • Switch to Signed RMS view
  • Focus on levels D3+ for cleaner signals

See Also​