The ADXVMA refers to the concepts introduced with the ADX (Average Directional Index) developed by Welles Wilder and the
VMA (
VIDYA Moving Average) created by Tushar Chande.
VMA:
The VMA is basically an exponential
moving average with an adaptive smoothing constant. For a standard exponential moving average the smoothing constant is k = 2/(n+1), where n is the period of the exponential moving average. Chande created an adaptive moving average by calculating a
volatility index vi and then replacing the smoothing constant k with the product k * vi. The resulting moving average is adaptive in the sense that the exponential smoothing is modulated by the volatility. The volatility index is derived from the (
CMO) Chande
Momentum Oscillator. The CMO is an oscillator which takes a value of 100, when the market is trending up, -100 when the market is trending down, and values around 0 when the market moves sideways. Thus the smoothing constant is reduced and the average gets slower during sideways markets.
ADXVMA:
There appears to be no direct link to the ADX formula. The indicator does not even use the true
range. However, all CMO, VMA and ADXVMA split the bar-to-bar moves into up moves and down moves, each of which are separately smoothed, before any ratios are calculated. You can consider the VMA as a nephew of the ADX. The ADXVMA is simply a modified VMA.
Chande's CMO uses a simple moving average to smooth both up moves and down moves. The ADXVMA has the simple moving average replaced with an exponential moving average. It then uses additional layers of exponential smoothing before the volatility index is calculated. Those additional layers slow the ADXVMA further down, when compared to the VMA.
The ADXVMA therefore lags compared to the VMA, it detects consolidation at a later stage, but once it has detected a consolidation it stays
flat for a longer time. I have attached a chart for comparing the two moving averages.
Source (with minor edits):
