Stochastic Chebyshev Smoothed With Zero Lag Smoothing

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Fast and Smooth Stochastic Oscillator with Zero Lag


In this post, we will discuss a custom implementation of a Stochastic Oscillator that not only smooths the signal but also does so without introducing any noticeable lag. This is a remarkable achievement, as it allows for a fast Stochastic Oscillator that is less prone to false signals without being slow and sluggish.

We will go through the code step by step, explaining the various functions and the overall structure of the code.

First, let's start with a brief overview of the Stochastic Oscillator and the problem it addresses.


The Stochastic Oscillator is a momentum indicator used in technical analysis to determine potential overbought or oversold conditions in an asset's price. It compares the closing price of an asset to its price range over a specified period. However, the Stochastic Oscillator is susceptible to false signals due to its sensitivity to price movements. This is where our custom implementation comes in, offering a smoother signal without noticeable lag, thus reducing the number of false signals.

Despite its popularity and widespread use in technical analysis, the Stochastic Oscillator has its share of drawbacks. While it is a price scaler that allows for easier comparisons across different assets and timeframes, it is also known for generating false signals, which can lead to poor trading decisions. In this section, we will delve deeper into the limitations of the Stochastic Oscillator and discuss the challenges associated with smoothing to mitigate its drawbacks.

Limitations of the Stochastic Oscillator

False Signals: The primary issue with the Stochastic Oscillator is its tendency to produce false signals. Since it is a momentum indicator, it reacts to short-term price movements, which can lead to frequent overbought and oversold signals that do not necessarily indicate a trend reversal. This can result in traders entering or exiting positions prematurely, incurring losses or missing out on potential gains.

Sensitivity to Market Noise: The Stochastic Oscillator is highly sensitive to market noise, which can create erratic signals in volatile markets. This sensitivity can make it difficult for traders to discern between genuine trend reversals and temporary fluctuations.

Lack of Predictive Power: Although the Stochastic Oscillator can help identify potential overbought and oversold conditions, it does not provide any information about the future direction or strength of a trend. As a result, it is often used in conjunction with other technical analysis tools to improve its predictive power.

Challenges of Smoothing the Stochastic Oscillator

To address the limitations of the Stochastic Oscillator, many traders attempt to smooth the indicator by applying various techniques. However, these approaches are not without their own set of challenges:

Trade-off between Smoothing and Responsiveness: The process of smoothing the Stochastic Oscillator inherently involves reducing its sensitivity to price movements. While this can help eliminate false signals, it can also result in a less responsive indicator, which may not react quickly enough to genuine trend reversals. This trade-off can make it challenging to find the optimal balance between smoothing and responsiveness.

Increased Complexity: Smoothing techniques often involve the use of additional mathematical functions and algorithms, which can increase the complexity of the indicator. This can make it more difficult for traders to understand and interpret the signals generated by the smoothed Stochastic Oscillator.

Lagging Signals: Some smoothing methods, such as moving averages, can introduce a time lag into the Stochastic Oscillator's signals. This can result in late entry or exit points, potentially reducing the profitability of a trading strategy based on the smoothed indicator.

Overfitting: In an attempt to eliminate false signals, traders may over-optimize their smoothing parameters, resulting in a Stochastic Oscillator that is overfitted to historical data. This can lead to poor performance in real-time trading, as the overfitted indicator may not accurately reflect the dynamics of the current market.

In our custom implementation of the Stochastic Oscillator, we used a combination of Chebyshev Type I Moving Average and zero-lag Gaussian-weighted moving average filters to address the indicator's limitations while preserving its responsiveness. In this section, we will discuss the reasons behind selecting these specific filters and the advantages of using the Chebyshev filter for our purpose.

Filter Selection

Chebyshev Type I Moving Average: The Chebyshev filter was chosen for its ability to provide a smoother signal without sacrificing much responsiveness. This filter is designed to minimize the maximum error between the original and the filtered signal within a specific frequency range, effectively reducing noise while preserving the overall shape of the signal. The Chebyshev Type I Moving Average achieves this by allowing a specified amount of ripple in the passband, resulting in a more aggressive filter roll-off and better noise reduction compared to other filters, such as the Butterworth filter.

Zero-lag Gaussian-weighted Moving Average: To further improve the Stochastic Oscillator's performance without introducing noticeable lag, we used the zero-lag Gaussian-weighted moving average (GWMA) filter. This filter combines the benefits of a Gaussian-weighted moving average, which prioritizes recent data points by assigning them higher weights, with a zero-lag approach that minimizes the time delay in the filtered signal. The result is a smoother signal that is less prone to false signals and is more responsive than traditional moving average filters.

Advantages of the Chebyshev Filter

Effective Noise Reduction: The primary advantage of the Chebyshev filter is its ability to effectively reduce noise in the Stochastic Oscillator signal. By minimizing the maximum error within a specified frequency range, the Chebyshev filter suppresses short-term fluctuations that can lead to false signals while preserving the overall trend.

Customizable Ripple Factor: The Chebyshev Type I Moving Average allows for a customizable ripple factor, enabling traders to fine-tune the filter's aggressiveness in reducing noise. This flexibility allows for better adaptability to different market conditions and trading styles.

Responsiveness: Despite its effective noise reduction, the Chebyshev filter remains relatively responsive compared to other smoothing filters. This responsiveness allows for more accurate detection of genuine trend reversals, making it a suitable choice for our custom Stochastic Oscillator implementation.

Compatibility with Zero-lag Techniques: The Chebyshev filter can be effectively combined with zero-lag techniques, such as the Gaussian-weighted moving average filter used in our custom implementation. This combination results in a Stochastic Oscillator that is both smooth and responsive, with minimal lag.

Code Overview

The code begins with defining custom mathematical functions for hyperbolic sine, cosine, and their inverse functions. These functions will be used later in the code for smoothing purposes.

Next, the gaussian_weight function is defined, which calculates the Gaussian weight for a given 'k' and 'smooth_per'. The zero_lag_gwma function calculates the zero-lag moving average with Gaussian weights. This function is used to create a Gaussian-weighted moving average with minimal lag.

The chebyshevI function is an implementation of the Chebyshev Type I Moving Average, which is used for smoothing the Stochastic Oscillator. This function takes the source value (src), length of the moving average (len), and the ripple factor (ripple) as input parameters.

The main part of the code starts by defining input parameters for K and D smoothing and ripple values. The Stochastic Oscillator is calculated using the ta.stoch function with Chebyshev smoothed inputs for close, high, and low. The result is further smoothed using the zero-lag Gaussian-weighted moving average function (zero_lag_gwma).

Finally, the lag variable is calculated using the Chebyshev Type I Moving Average for the Stochastic Oscillator. The Stochastic Oscillator and the lag variable are plotted on the chart, along with upper and lower bands at 80 and 20 levels, respectively. A fill is added between the upper and lower bands for better visualization.


The custom Stochastic Oscillator presented in this blog post combines the Chebyshev Type I Moving Average and zero-lag Gaussian-weighted moving average filters to provide a smooth and responsive signal without introducing noticeable lag. This innovative implementation results in a fast Stochastic Oscillator that is less prone to false signals, making it a valuable tool for technical analysts and traders alike.

However, it is crucial to recognize that the Stochastic Oscillator, despite being a price scaler, has its limitations, primarily due to its propensity for generating false signals. While smoothing techniques, like the ones used in our custom implementation, can help mitigate these issues, they often introduce new challenges, such as reduced responsiveness, increased complexity, lagging signals, and the risk of overfitting.

The selection of the Chebyshev Type I Moving Average and zero-lag Gaussian-weighted moving average filters was driven by their combined ability to provide a smooth and responsive signal while minimizing false signals. The advantages of the Chebyshev filter, such as effective noise reduction, customizable ripple factor, and responsiveness, make it an excellent fit for addressing the limitations of the Stochastic Oscillator.

When using the Stochastic Oscillator, traders should be aware of these limitations and challenges, and consider incorporating other technical analysis tools and techniques to supplement the indicator's signals. This can help improve the overall accuracy and effectiveness of their trading strategies, reducing the risk of losses due to false signals and other limitations associated with the Stochastic Oscillator.

Feel free to use, modify, or improve upon this custom Stochastic Oscillator code in your trading strategies. We hope this detailed walkthrough of the custom Stochastic Oscillator, its limitations, challenges, and filter selection has provided you with valuable insights and a better understanding of how it works. Happy trading!
removed extra smoothing by default


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