Autoregressive integrated moving-average ARIMA(p, d, q) models combine AR(p) and MA(q) processes to leverage the complementarity of these building blocks and simplify model development by using a more compact form and reducing the number of parameters, in turn reducing the risk of overfitting.

The models also take care of eliminating unit-root nonstationarity by using the d^th difference of the time series values. An ARIMA(p, 1, q) model is the same as using an ARMA(p, q) model with the first differences of the series. Using y' to denote the original series after non-seasonal differencing d times, the ARIMA(p, d, q) model is simply:

ARIMA models are also estimated using Maximum Likelihood. Depending on the implementation, higher-order models may generally subsume lower-order models. For example, statsmodels includes all lower-order p and q terms and does not permit removing coefficients for lags below the highest value. In this case, higher-order models will always fit better. Be careful not to overfit your model to the data by using too many terms.