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The equation for ARIMA(1,1,1) is $Z_t = \phi_1 Z_{t-1} + \theta_1 \epsilon_{t-1} + \epsilon_t$, where $Z_t$ is the differenced series, $\phi_1$ is the autoregressive coefficient, $\theta_1$ is the moving-average coefficient, and $\epsilon_t$ is the error term.

Conditions: The model is ARIMA(1,1,1).; $Z_t$ is the first difference of the original series $q_t$.; $p=1, d=1, q=1$.

The equation for ARIMA(1,1,1) is $Z_t = \phi_1 Z_{t-1} + \theta_1 \epsilon_{t-1} + \epsilon_t$, where $Z_t$ is the differenced series, $\phi_1$ is the autoregressive coefficient, $\theta_1$ is the moving-average coefficient, and $\epsilon_t$ is the error term.

Conditions: The model is ARIMA(1,1,1).; $Z_t$ is the first difference of the original series $q_t$.; $p=1, d=1, q=1$.