Wavelet Transform and why people used it to denoise 1min chart and its comparison with Fourier Transform – Analytics & Forecasts – 29 April 2025

📈 What’s a Wavelet Rework in buying and selling analysis?

Wavelet Rework is a mathematical device that breaks down a value collection into totally different frequency parts — however localized in time.

• Consider it like a microscope for charts:
  it helps you zoom into totally different time scales at totally different moments.

• In contrast to a Fourier Rework (which supplies you solely total cycle/frequency information however loses time information),
  Wavelet Rework retains each:
  — what frequencies exist
  — and when they happen.

🧠 In easy phrases:

🛠️ In buying and selling analysis, folks use Wavelet Transforms to:

• Detect pattern shifts (as a result of totally different wavelet ranges present developments vs noise individually)

• Discover cyclical patterns that are not fixed (adaptive cycles)

• Denoise value information (eradicating ineffective small noise whereas protecting necessary swings)

• Examine volatility clustering (volatility is not fixed over time)

• Create higher technical indicators (wavelet-smoothed shifting averages, wavelet-based MACD, and so on.)

• Enhance forecasting fashions (enter clear information into Machine Studying fashions)

🔥 Instance use case:

You could have messy 1-minute Bitcoin costs.
You apply a Wavelet Decomposition, and cut up it into:

• Low-frequency part → most important market pattern

• Excessive-frequency parts → noise, mean-reversion, short-term spikes

Then you possibly can:

• Commerce the pattern utilizing low-frequency wavelet

• Imply-revert scalp utilizing high-frequency spikes

• Filter out noise when constructing fashions

⚡ Kinds of Wavelet Transforms merchants discover:

• Discrete Wavelet Rework (DWT)
  → breaks the sign into mounted layers/scales

• Steady Wavelet Rework (CWT)
  → extra detailed however computationally heavier

• Wavelet Packet Rework (WPT)
  → deeper decomposition (each approximation and element ranges are cut up)

Largely, DWT is sensible for buying and selling as a result of it is quick sufficient.

📚 Good references if you wish to dive deeper:

• “Wavelet Purposes in Monetary Engineering” (tutorial papers)

• Folks like Tucker Balch (early ML buying and selling analysis) used wavelets of their methods.

• Some hedge funds have used wavelet preprocessing earlier than feeding costs into neural networks.