Average true range
Average true range (ATR) is a technical analysis volatility indicator originally developed by J. Welles Wilder, Jr. for commodities. The indicator does not provide an indication of price trend, simply the degree of price volatility. The average true range is an N-day smoothed moving average (SMMA) of the true range values. Wilder recommended a 14-period smoothing.
The range of a day's trading is simply . The true range extends it to yesterday's closing price if it was outside of today's range.
The true range is the largest of the:
The ATR at the moment of time t is calculated using the following formula: (This is one form of an exponential moving average)
The first ATR value is calculated using the arithmetic mean formula:
The idea of ranges is that they show the commitment or enthusiasm of traders. Large or increasing ranges suggest traders prepared to continue to bid up or sell down a through the course of the day. Decreasing range suggests waning interest.
Since true range and ATR are calculated by subtracting prices, the volatility they compute does not change when historical prices are back-adjusted by adding or subtracting a constant to every price. Back-adjustments are often employed when splicing together individual monthly futures contracts to form a continuous futures contract spanning a long period of time. However the standard procedures used to compute volatility of stock prices, such as the standard deviation of logarithmic price ratios, are not invariant (to addition of a constant). Thus futures traders and analysts typically use one method (ATR) to calculate volatility, while stock traders and analysts typically use another (SD of log price ratios).
...
Wikipedia