J. Welles Wilder Smoothing Average

Parameters: period = 14 (2–200)

Overview

The J. Welles Wilder Smoothing Average (JSA), also known as Wilder's Smoothing or Smoothed Moving Average (SMMA), was introduced in the 1978 book "New Concepts in Technical Trading Systems." This smoothing method is fundamental to many of Wilder's famous indicators including the Relative Strength Index (RSI), Average True Range (ATR), Average Directional Index (ADX), and Parabolic SAR.

What makes Wilder's smoothing distinctive is its recursive calculation and unique weighting system. An n-period Wilder's smoothing is mathematically equivalent to a (2n-1) period Exponential Moving Average. For example, a 14-period Wilder's smoothing (the default for RSI) provides the same smoothing as a 27-period EMA. This relationship allows traders to convert between the two methods while maintaining mathematical equivalence.

Interpretation & Trading Signals

Smoothing Characteristics:

  • Recursive Formula: WWS(t) = WWS(t-1) + ((Price(t) - WWS(t-1)) / Period)
  • EMA Equivalent: n-period Wilder = (2n-1) period EMA
  • Weight Distribution: Historical prices weighted more heavily than recent
  • Initialization: First value = simple average of first n bars

Trading Applications:

  • Trend Following: Slower response ideal for long-term trend identification
  • Noise Reduction: Filters daily fluctuations and market noise effectively
  • Indicator Foundation: Core component of RSI, ATR, ADX calculations
  • Consistent Behavior: Predictable lag and smoothing characteristics

Key Advantages & Limitations:

  • Advantages: Clear long-term trends, reduced false signals, stability
  • Limitations: Lags behind price movement, slower to respond to reversals
  • Best Markets: Trending markets with sustained directional moves
  • Default Period: 14 (as recommended by Wilder for most indicators)

Example Usage

Code examples will be available once the Rust implementation is complete.

Performance Analysis

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