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You would use a second difference if the first differenced series is still not stationary. The goal is to choose the lowest differencing order $d$ that makes the series stationary.

Conditions: The original series is non-stationary.; First differencing ($d=1$) does not result in a stationary series.; The modeler can inspect the stationarity of the differenced plots.

You would use a second difference if the first differenced series is still not stationary. The goal is to choose the lowest differencing order $d$ that makes the series stationary.

Conditions: The original series is non-stationary.; First differencing ($d=1$) does not result in a stationary series.; The modeler can inspect the stationarity of the differenced plots.

The $d$ in ARIMA(p,d,q) represents the order of differencing, also known as the integrated component. It indicates how many times the original series has been differenced to achieve stationarity.

Conditions: The model is denoted as ARIMA(p,d,q).; $d$ is a non-negative integer.

The $d$ in ARIMA(p,d,q) represents the order of differencing, also known as the integrated component. It indicates how many times the original series has been differenced to achieve stationarity.

Conditions: The model is denoted as ARIMA(p,d,q).; $d$ is a non-negative integer.