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Variable (or Volatility) Index Dynamic Average. Also known as VMA as in V(idya) Moving Average.

Variable Index Dynamic Average (VIDYA) is a special moving average which was developed by Tushar Chande. The complete details about this technical indicator can be found in The New Technical Trader by Tushar Chande and Stanley Kroll.

VIDYA is essentially a dynamic exponential moving average wherein the market volatility is also taken into consideration; this is achieved by using Chande Momentum Oscillator (CMO) as a measure of market volatility. The averaging period depends on the market volatility, and VIDYA moves faster as the short-term volatility increases, whereas it slows down when market volatility decreases.

This indicator needs two input parameters (a) Time period over which VIDYA needs to be averaged and (b) Time period over which volatility has to be estimated, basically this is the period over which CMO is calculated.

VIDYA is calculated in the following way:

First of all CMO is calculated using the following formula:

CMO(i) = (UpSum(i) - DnSum(i))/(UpSum(i) + DnSum(i))

where:

UpSum(i) - current sum of positive price increments for the given period;
DnSum(i) - current sum of negative price increments for the given period.

This CMO is then used to estimate VIDYA

VIDYA(i) = Price(i) * F * ABS(CMO(i)) + VIDYA(i-1) * (1 - F* ABS(CMO(i)))

where:

F = 2/(Period_EMA+1) - smoothing factor;
ABS(CMO(i)) - absolute current value CMO;
VIDYA(i-1) - previous value of VIDYA.

Read more: https://www.quantshare.com/item-1034-vidya-variable-index-dynamic-average

See also:
https://www.metatrader5.com/en/terminal/help/indicators/trend_indicators/vida
https://www.blastchart.com/Community/IndicatorGuide/Indicators/VIDYA.aspx
https://fxcodebase.com/wiki/index.php/Chande's_Variable_Index_Dynamic_Average_(VIDYA)

For a blast from the past, see this: https://blog.bigmiketrading.com/2009/04/simple-vma-strategy.html

Reference book: https://store.traders.com/-v10-c03-adaptin-pdf.html

A related indicator is the ADXVMA

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