The Exponential Standard Deviation (ESD) Bands are a volatility-band technical indicator proposed by Vitali Apirine. This indicator comprises two lines (bands) plotted, by default, two exponential standard deviations above and below an exponential moving average. The exponential standard deviation is equal to the root mean square of price deviations from its exponential moving average.

The interpretation of ESD Bands involves several techniques:

  • Volatility analysis. In ESD Bands, the concept of volatility is based on the exponential standard deviation: the higher the volatility, the greater the deviation. Thus, the distance between the bands increases when the volatility level rises. Conversely, when the volatility decreases, the bands converge.
  • Trend analysis. ESD Bands are trend-following and lag price action as the exponential moving average is used in the calculation. The bands tend to move upward in uptrends and downward in downtrends. In sideways trends, the bands move horizontally.
  • Trend reversal detection. The distance between the bands is generally substantial to keep the price plot inside. However, the price may be sometimes seen pierce either band indicating a possible trend reversal or emergence. When the bands move upward and the price rises above the upper band, the start of an uptrend is possible. Piercing the lower band when the bands are in downturn might signify the start of a downtrend.
  • Sideways trend analysis. When the trend is flat and the bands move in the horizontal direction, the price can be often seen form a peak at the upper band and a trough at the lower one.

Input Parameters

price The type of price for which the exponential standard deviation is calculated.
length The period with which the average and the exponential standard deviation are calculated.
displace The displacement of the ESD Bands plots, in bars. Positive values signify backward displacement.
num dev dn The distance between the moving average and the lower band, measured in exponential standard deviations.
num dev up The distance between the moving average and the upper band, measured in exponential standard deviations.


UpperBand The upper ESD band.
MidLine The exponential moving average.
LowerBand The lower ESD band.

Further Reading

1. "Exponential Standard Deviation Bands" by Vitali Apirine. Technical Analysis of Stocks & Commodities, February 2017.


*For illustrative purposes only. Not a recommendation of a specific security or investment strategy.

  Past performance is no guarantee of future performance.

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