Variety N-Tuple Moving Averages w/ Variety Stepping

The Variety N-Tuple Moving Averages w/ Variety Stepping indicator calculates highly customizable moving averages ranging from 1 to 30 tuples while offering advanced volatility-based stepping and filtering. It provides a streamlined, computationally efficient method to generate complex moving average types like Double-EMA, Triple-EMA, or higher-order N-tuple variations combined with multiple band and signal options.

Usage

The Usage section describes how the script can be used, examples should be provided in this section. This section also focuses on how main settings affect the indicator interpretation and output.

The indicator is primarily used to identify trend direction and momentum through high-order smoothing. Users can select the "Depth" to determine the order of the moving average (e.g., a depth of 3 creates a Triple Moving Average).

The "Stepping" feature filters out market noise. If the price or moving average does not move beyond a specific threshold (defined by the chosen deviation type and multiplier), the value remains unchanged from the previous bar, resulting in a "staircase" effect during consolidation.

Examples of usage:

• Trend Identification: A green line indicates an uptrend, while a red line indicates a downtrend.
• Volatility Filtering: Using "Adaptive Deviation" stepping can help traders avoid whipsaws in choppy markets by requiring a specific volatility-adjusted move before the indicator updates.
• Mean Reversion: Utilizing the built-in bands (e.g., ATR or Standard Deviation) helps identify potential overextended price levels relative to the N-tuple average.

Details

The indicator utilizes a streamlined looping solution and arrays to calculate weighted nested moving averages without excessive memory consumption. The process follows three main steps:

1. Factorial Calculation: The script runs a factorial calculation based on the user-defined depth.
2. Weight Assignment: It calculates the weights of nested moving averages using the formula factorial(depth) / (factorial(depth - k) * factorial(k)).
3. Coefficient Application: These coefficients are applied to the sequence of MAs. For example, a 5-depth EMA (Quintuple EMA) calculation follows the structure: 5 * ema1 - 10 * ema2 + 10 * ema3 - 5 * ema4 + ema5.

The stepping logic employs various statistical measures (ATR, Standard Deviation, Adaptive Deviation, etc.) to evaluate if current movement is significant enough to warrant an update in the indicator's output value.

Settings

Basic Settings

• Period: The lookback period used for the base moving average calculation.
• Depth: Determines the tuple order (1-50). Higher values increase smoothing and lag.
• Moving Average Type: Choose between Exponential Moving Average (EMA) or Running Moving Average (RMA).

Filter Settings

• Price Filter Type: Selects the statistical method for filtering the input source (ATR, Standard Deviation, etc.).
• Moving Average Filter Type: Selects the statistical method for filtering the MA output.
• Filter Options: Choose whether to apply the filter to the Price, the MA, Both, or None.
• Filter Multiplier: Adjusts the sensitivity of the stepping filter.
• Filter Period: The lookback period for the chosen filter type.

Bands Settings

• Band Type: Determines the calculation method for the outer channels.
• Band Multiplier: Sets the width of the channels.

UI Options

• Color bars?: Toggles price bar coloring based on trend state.
• Show signals?: Toggles the "L" (Long) and "S" (Short) labels on the chart.
• Show bands?: Toggles the visibility of volatility channels.

FAQ

What is an N-tuple Moving Average? It is a moving average that has been smoothed multiple times by itself. For example, a 2-tuple is a Double MA, and a 3-tuple is a Triple MA. This indicator allows for up to 30 levels of nested smoothing.

How do the stepping functions help? Stepping functions act as a volatility filter. They prevent the indicator from reacting to minor price fluctuations, helping to stay in a trend until a significant move occurs in the opposite direction.

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