STD-Stepped, Variety N-Tuple Moving Averages

The STD-Stepped, Variety N-Tuple Moving Averages indicator provides a standard deviation-filtered N-tuple moving average that allows users to create deeply nested smoothing structures from double up to 15-tuple layers. This tool aims to reduce lag while maintaining smoothness by applying a factorial-based weighting system to multiple iterations of a base moving average, further refined by a standard deviation stepping filter.

Usage

The Usage section describes how the script can be used to create custom smoothing profiles. By selecting a base moving average type (such as EMA) and increasing the "Depth," users can create advanced versions of standard indicators; for example, an EMA with a depth of 2 is equivalent to a DEMA, while a depth of 3 results in a TEMA.

The indicator features a "Standard Deviation Stepping" filter, which allows the moving average to remain flat (stepped) until the price or the average itself moves beyond a specific standard deviation threshold. This is particularly useful for filtering out market noise during consolidation phases. Users can choose to apply the filter to the price, the N-tuple moving average (NTMA), or both.

Details

The script operates through a three-step mathematical process:

1. Factorial Calculation: It runs a factorial calculation on the user-defined depth value.
2. Weighting: It calculates the weights of the nested moving averages using the formula: factorial(depth) / (factorial(depth - k) * factorial(k)), where k represents the weight position.
3. Coefficient Application: Each layer of the moving average is calculated sequentially (e.g., EMA1, then EMA2 of EMA1, etc.), and the calculated coefficients are applied to produce the final N-tuple result.

This implementation includes 5 base moving average types (EMA, WMA, SMA, RMA, and T3) and supports extended source types, including Heiken-Ashi and better-smoothed variants.

Settings

• Heiken-Ashi Better Smoothing: Selects the smoothing algorithm for source calculations (AMA, T3, or Kaufman).
• Source: Choose the price data input, including standard options and various Heiken-Ashi derived sources.
• Period: Sets the lookback period for the base moving average calculation.
• Depth: Determines the number of nested layers (1-15). Higher values increase the complexity of the N-tuple calculation.
• Variety Moving Average Type: The base algorithm used for nesting (EMA, WMA, SMA, RMA, or T3).
• T3 Settings: Adjusts the "Hotness" and calculation type (New vs. Original) specifically for the T3 moving average.
• Filter Options: Determines if the standard deviation step filter is applied to "Price," "NTMA," "Both," or "None."
• Filter Deviations: The multiplier for the standard deviation filter to determine the stepping threshold.
• Filter Period: The lookback window used to calculate the standard deviation for the filter.
• UI Options: Toggles for bar coloring and visual buy/sell signals on the chart.
• Moving Average Inputs: Specific parameters for Kaufman's Adaptive MA (KAMA) and Adaptive Moving Average (AMA).

FAQ

How do I interpret the "Depth" setting? The Depth setting determines how many times the moving average is nested. A depth of 1 is a standard MA, while higher depths create more responsive, zero-lag style averages like DEMA (Depth 2) or TEMA (Depth 3).

What does the "Stepping" do? The stepping mechanism acts as a volatility filter. If the price movement is within the "Filter Deviations" range, the indicator line remains horizontal, helping traders avoid "whipsaws" in sideways markets.

How can I access this indicator? You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.