Wavelet Decomposition

Wavelet Decomposition takes a series apart by timescale and proves the parts add back up — the library's first faithful implementation of wavelet decomposition. A shift-invariant transform splits a rolling window into detail levels, each an octave of fluctuation (D1 spans 2-4 bars, D2 4-8, and so on), plus an approximation of everything slower. Details stack in the pane on a shared amplitude scale, denoised and trend reconstructions draw over price, and an energy table ranks the scales, its last row verifying the additive identity.

How to Trade the Wavelet Decomposition?

• Denoised crosses: price crossing the denoised reconstruction — approximation plus surviving details — is alerted both ways.
• Trend turns: the approximation's slope flipping sign is alerted — the trend-extraction use.
• Dominant scale: the strongest table shading marks the level with the most detail energy; a shift there is alerted.
• Boundary zone: the shaded right edge comes from padded data and revises — provisional by construction.

Wavelet Decomposition Settings

• Source (default close): the series decomposed.
• Analysis Window (default 256): rolling bars the pyramid recomputes over.
• Levels (J) (default 4): depth, auto-reduced when the deepest filter no longer fits the window.
• Wavelet Family (default Daubechies-4): Haar is simplest and most edge-friendly; Daubechies filters smooth more with wider boundary effects.
• Boundary Handling (default Reflection): mirror the sample edges, or wrap with Periodic.
• Suppress Finest Levels (K) (default 2) and Denoise Mode (default Suppress): zero the K fastest levels, or shrink their coefficients with Soft Threshold's median-based universal threshold.
• Display (all on): Denoised Reconstruction, Trend (Approximation), Detail Stack, Energy Table and Boundary Zone; Line Width (default 2).

Frequently Asked Questions

Why use wavelets instead of a Kalman filter?

A Kalman Filter runs a recursive model forward — one smoothed state per bar, never revised. Wavelets analyze a whole window at once and separate every timescale: richer, but with edge values that revise as the window rolls.

What exactly is the boundary problem?

The filters need data beyond both sample ends, so edges are padded by reflection or wrap-around; padded values revise as real bars replace them. The build shades the region and repeats the caveat in its alerts.

Which wavelet family should I choose?

Daubechies-4 is the common default: smoother than Haar at modest filter length. Haar minimizes edge effects and follows sharp moves best; Daubechies-6 smooths further with a wider revising edge.