Wavelet Filter with Adaptive Upsampling [BackQuant]Wavelet Filter with Adaptive Upsampling
The Wavelet Filter with Adaptive Upsampling is an advanced filtering and signal reconstruction tool designed to enhance the analysis of financial time series data. It combines wavelet transforms with adaptive upsampling techniques to filter and reconstruct price data, making it ideal for capturing subtle market movements and enhancing trend detection. This system uses high-pass and low-pass filters to decompose the price series into different frequency components, applying adaptive thresholding to eliminate noise and preserve relevant signal information.
Shout out to Loxx for the Least Squares fitting of trigonometric series and Quinn and Fernandes algorithm for finding frequency
www.tradingview.com
Key Features
1. Frequency Decomposition with High-Pass and Low-Pass Filters:
The indicator decomposes the input time series using high-pass and low-pass filters to separate the high-frequency (detail) and low-frequency (trend) components of the data. This decomposition allows for a more accurate analysis of underlying trends, while mitigating the impact of noise.
2. Soft Thresholding for Noise Reduction:
A soft thresholding function is applied to the high-frequency component, allowing for the reduction of noise while retaining significant market signals. This function adjusts the coefficients of the high-frequency data, removing small fluctuations and leaving only the essential price movements.
3. Adaptive Upsampling Process:
The upsampling process in this script can be customized using different methods: sinusoidal upsampling, advanced upsampling, and simple upsampling. Each method serves a unique purpose:
Sinusoidal Upsample uses a sine wave to interpolate between data points, providing a smooth transition.
Advanced Upsample utilizes a Quinn-Fernandes algorithm to estimate frequency and apply more sophisticated interpolation techniques, adapting to the market’s cyclical behavior.
Simple Upsample linearly interpolates between data points, providing a basic upsampling technique for less complex analysis.
4. Reconstruction of Filtered Signal:
The indicator reconstructs the filtered signal by summing the high and low-frequency components after upsampling. This allows for a detailed yet smooth representation of the original time series, which can be used for analyzing underlying trends in the market.
5. Visualization of Reconstructed Data:
The reconstructed series is plotted, showing how the upsampling and filtering process enhances the clarity of the price movements. Additionally, the script provides the option to visualize the log returns of the reconstructed series as a histogram, with positive returns shown in green and negative returns in red.
6. Cumulative Series and Trend Detection:
A cumulative series is plotted to visualize the compounded effect of the filtered and reconstructed data. This feature helps traders track the overall performance of the asset over time, identifying whether the asset is following a sustained upward or downward trend.
7. Adaptive Thresholding and Noise Estimation:
The system estimates the noise level in the high-frequency component and applies an adaptive thresholding process based on the standard deviation of the downsampled data. This ensures that only significant price movements are retained, further refining the trend analysis.
8. Customizable Parameters for Flexibility:
Users can customize the following parameters to adjust the behavior of the indicator:
Frequency and Phase Shift: Control the periodicity of the wavelet transformation and the phase of the upsampling function.
Upsample Factor: Adjust the level of interpolation applied during the upsampling process.
Smoothing Period: Determine the length of time used to smooth the signal, helping to filter out short-term fluctuations.
References
Enhancing Cross-Sectional Currency Strategies with Context-Aware Learning to Rank
arxiv.org
Daubechies Wavelet - Wikipedia
en.wikipedia.org
Quinn Fernandes Fourier Transform of Filtered Price by Loxx
Note on Usage for Mean-Reversion Strategy
This indicator is primarily designed for trend-following strategies. However, by taking the inverse of the signals, it can be adapted for mean-reversion strategies. This involves buying underperforming assets and selling outperforming ones. Caution: This method may not work effectively with highly correlated assets, as the price movements between correlated assets tend to mirror each other, limiting the effectiveness of mean-reversion strategies.
Final Thoughts
The Wavelet Filter with Adaptive Upsampling is a powerful tool for traders seeking to improve their understanding of market trends and noise. By using advanced wavelet decomposition and adaptive upsampling, this system offers a clearer, more refined picture of price movements, enhancing trend-following strategies. It’s particularly useful for detecting subtle shifts in market momentum and reconstructing price data in a way that removes noise, providing more accurate insights into market conditions.
