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The indicator is based on the true range, which is the maximum of (High - Low), Abs (High - Close [1]) and Abs (Low - Close [1]), where Abs is the mathematical absolute value.
To get the first data, it calculates the true range values ​​for multiple bars (i.e. the input length) and then calculates the SMA of these values ​​(i.e. the sum of all these values ​​divided by the length - the simple average). This average is set as the first ATR value.

Smoothing method:

RMA: Coefficient alpha is defined as: alpha = 1/Length. RMA is calculated as: rma = alpha * (true range value of the candle) + (1-alpha) * (last rma).
SMA: For each bar, it calculates the simple average of the true range values ​​for a defined number (length) of bars. This mode is equal to the iATR value.
EMA: Coefficient alpha is defined as: alpha = 2/(1+Length). The calculation formula of EMA is: ema = alpha * (the true range value of the candle) + (1-alpha) * (the last ema).
WMA: For each bar, it calculates the weighted average of the true range values ​​for the defined number (length) of bars as follows:
Sum = N * (tr[0]) + (N-1) * (tr[1]) + ... + 1 * (tr[N-1]); tr is the true range value of the candle
wma = sum/ (N*(N+1)/2)

Example: XAUUSD, H1

Attachment download

📎 atr-with-smoothing.mq4 (4.46 KB)

Source: MQL5 #36438