# Window Aggregate EMA

> The Exponential Moving Average (EMA) is calculated using the following iterative algorithm, where `n` is the “number of days” for the moving average (starting with 1):

>         p = 2 / (interval+1)
>         EMA[0] = input[0] * p
>         EMA[n] = EMA[n-1] * (1–p)

> For example, applying the EMA 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:

>         {335.000000, 453.250000, 351.187500, 363.890625, 455.917969, 353.938477,
>         466.703857, 462.527893, 443.145920, 437.359440, 419.769580, 332.077185}

> The valid windows can be verified using the following table (built with Microsoft Excel version 2010 or later) where `p = 2/8 = 0.25`:

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