# Window Aggregate ATR

> The Average True Range (ATR) is calculated using the algorithm described in the following Wikipedia page: http://en.wikipedia.org/wiki/Moving_average

> The true range is the largest of the:

> - Most recent period's high minus the most recent period's low
> - Absolute value of the most recent period's high minus the previous close
> - Absolute value of the most recent period's low minus the previous close

> The ATR at the moment of time `t` is expressed by the following formula:

> The first ATR value is expressed with the arithmetic mean formula:

> The eXtremeDB runtime computes the ATR using following iterative formula:

>         ATR[i] = ATR[i-1] * (n-1)

> where

>         n = min( i+1, window_size )

> For example, applying the ATR calculation to the following input sequence of values:

>         {335, 808, 45, 402, 732, 48, 805, 450, 385, 420, 367, 69}

> with the interval argument of `7` produces the following result sequence:

>         {335, 571.5, 396, 397.5, 464.4, 395,
>         453.571429, 453.061224, 443.338192, 440.004165, 429.574999, 378.064284}

> Note that the first 6 values (highlighted above) should be ignored for this interval of 7 (see note in the Window versus Grid Aggregate page).