Cosine smoothed stochastic

25 Jun

Description
The "Cosine Smoothed Stochastic" indicator leverages advanced Fourier Transform techniques to smooth the traditional Stochastic Oscillator. This approach enhances the signal's reliability and reduces noise, providing traders with a more refined and actionable indicator.

The Stochastic Oscillator is a popular momentum indicator that measures the current price relative to the high-low range over a specified period. It helps identify overbought and oversold conditions, signaling potential trend reversals. By smoothing this indicator with Fourier Transform techniques, we aim to reduce false signals and improve its effectiveness.

The indicator comprises three main components:

Cosine Function: A custom function to compute the cosine of an input scaled by a frequency tuner.
Kernel Function: Utilizes the cosine function to create a smooth kernel, constrained to positive values within a specific range.
Kernel Regression and Multi Cosine: Perform kernel regression over a lookback period, with the multi cosine function summing these regressions at varying frequencies for a composite smooth signal.
Additionally, the indicator includes a volume oscillator to complement the smoothed stochastic signals, providing insights into market volume trends.

Features
Fourier Transform Smoothing: Advanced smoothing technique to reduce noise.
Volume Oscillator: Dynamic volume-based oscillator for additional market insights.
Customizable Inputs: Users can configure key parameters like regression lookback period, tuning coefficient, and smoothing length.
Visual Alerts: Buy and sell signals based on smoothed stochastic crossovers.
Usage

The indicator is designed for trend-following and momentum-based trading strategies. It helps identify overbought and oversold conditions, trend reversals, and potential entry and exit points based on smoothed stochastic values and volume trends.

Inputs
Cosine Kernel Setup:
varient: Choose between "Tuneable" and "Stepped" regression types.
lookbackR: Lookback period for regression.
tuning: Tuning coefficient for frequency adjustment.
Stochastic Calculation:
volshow: Toggle to show the volume oscillator.
emalength: Smoothing period for the Stochastic Oscillator.
lookback_period, m1, m2: Parameters for the Stochastic Oscillator lookback and moving averages.
How It Works
Stochastic Oscillator:
Computes the stochastic %K and smoothes it with an EMA.
Further smoothes %K using the multi cosine function.
Volume Oscillator:
Calculates short and long EMAs of volume and derives the oscillator as the percentage difference.
Plots volume oscillator columns with dynamic coloring based on the oscillator's value and change.
Visual Representation:
Plots smoothed stochastic lines with colors indicating bullish, bearish, overbought, and oversold conditions.
Uses plotchar to mark crossovers between current and previous values of d.
Displays overbought and oversold levels with filled regions between them.
Chart Example
To understand the indicator better, refer to the clean and annotated chart provided. The script is used without additional scripts to maintain clarity. The chart includes:

Smoothed Stochastic Lines: Colored according to trend conditions.
Volume Oscillator: Plotted as columns for visual volume trend analysis.
Overbought/Oversold Levels: Clearly marked levels with filled regions between them.
Alert Conditions
The indicator sets up alerts for buy and sell signals when the smoothed stochastic crosses over or under its previous value. These alerts can be used for automated trading systems or manual trading signals.


breakthrough of the indicators method :

Initialization and Inputs:

The indicator starts by defining necessary inputs, such as the lookback period for regression, tuning coefficient, and smoothing parameters for the Stochastic Oscillator and volume oscillator.

Cosine Function and Kernel Creation:

The cosine function is defined to compute the cosine of an input scaled by a frequency tuner.
The kernel function utilizes this cosine function to create a smoothing kernel, which is constrained to positive values within a specific range.
Kernel Regression:

The kernel regression function iterates over the lookback period, calculating weighted sums of the source values using the kernel function. This produces a smoothed value by dividing the accumulated weighted values by the total weights.
Multi Cosine Smoothing:

The multi cosine function combines multiple kernel regressions at different frequencies, summing these results and averaging them to achieve a composite smoothed value.
Stochastic Calculation and Smoothing:

The traditional Stochastic Oscillator is calculated, and its %K value is smoothed using an EMA.
The smoothed %K is further refined using the multi cosine function, resulting in a more reliable and less noisy signal.
Volume Oscillator Calculation:

The volume oscillator calculates short and long EMAs of the volume and derives the oscillator as the percentage difference between these EMAs. The result is plotted with dynamic coloring to indicate volume trends.
Plotting and Alerts:

The indicator plots the smoothed stochastic lines, overbought/oversold levels, and volume oscillator on the chart.
Buy and sell alerts are set up based on crossovers of the smoothed stochastic values, providing traders with actionable signals.