Kaiser Window MAKaiser Window Moving Average Indicator
The Kaiser Window Moving Average is a technical indicator that implements the Kaiser window function in the context of a moving average. This indicator serves as an example of applying the Kaiser window and the modified Bessel function of the first kind in technical analysis, providing an open-source implementation of these functions in the TradingView Pine Script ecosystem.
Key Components
Kaiser Window Implementation
This indicator incorporates the Kaiser window, a parameterized window function with certain frequency response characteristics. By making this implementation available in Pine Script, it allows for exploration and experimentation with the Kaiser window in the context of financial time series analysis.
Modified Bessel Function of the First Kind
The indicator includes an implementation of the modified Bessel function of the first kind, which is integral to the Kaiser window calculation. This mathematical function is now accessible within TradingView, potentially useful for other custom indicators or studies.
Customizable Alpha Parameter
The indicator features an adjustable alpha parameter, which directly influences the shape of the Kaiser window. This parameter allows for experimentation with the indicator's behavior:
Lower alpha values: The indicator's behavior approaches that of a Simple Moving Average (SMA)
Moderate alpha values: The behavior becomes more similar to a Weighted Moving Average (WMA)
Higher alpha values: Increases the weight of more recent data points
In signal processing terms, the alpha parameter affects the trade-off between main-lobe width and side lobe level in the frequency domain.
Centered and Non-Centered Modes
The indicator offers two operational modes:
Non-Centered (Real-time) Mode: Uses half of the Kaiser window, starting from the peak. This mode operates similarly to traditional moving averages, suitable for real-time analysis.
Centered Mode: Utilizes the full Kaiser window, resulting in a phase-correct filter. This mode introduces a delay equal to half the window size, with the plot automatically offset to align with the correct time points.
Visualization Options
The indicator includes several visualization features to aid in analysis:
Gradient Coloring: Offers three gradient options:
• Three-color gradient: Includes a neutral color
• Two-color gradient: Traditional up/down color scheme
• Solid color: For a uniform appearance
Glow Effect: An optional visual enhancement for the moving average line.
Background Fill: An option to fill the area between the moving average and the price.
Use Cases
The Kaiser Window Moving Average can be applied similarly to other moving averages. Its primary value lies in providing an example implementation of the Kaiser window and modified Bessel function in TradingView. It serves as a starting point for traders and analysts interested in exploring these mathematical concepts in the context of technical analysis.
Conclusion
The Kaiser Window Moving Average indicator demonstrates the application of the Kaiser window function in a moving average calculation. By providing open-source implementations of the Kaiser window and the modified Bessel function of the first kind, this indicator contributes to the expansion of available mathematical tools in the TradingView Pine Script environment, potentially facilitating further experimentation and development in technical analysis.
Factorial
combinLibrary "combin"
Description:
The combin function is a the combination function
as it calculates the number of possible combinations for two given numbers.
This function takes two arguments: the number and the number_chosen.
For example, if the number is 5 and the number chosen is 1,
there are 5 combinations, giving 5 as a result.
Reference:
ideone.com
support.microsoft.com
combin(n, kin)
Returns the number of combinations for a given number of items. Use to determine the total possible number of groups for a given number of items.
Parameters:
n : int, The number of items.
kin : int, The number of items in each combination.
Returns: int.
