Finding the best-fitting ARIMA model with auto-ARIMA
As we have seen in the previous recipe, the performance of an ARIMA model varies greatly depending on the chosen hyperparameters (p, d, and q). We can do our best to choose them based on our intuition, the statistical tests, and the ACF/PACF plots. However, this can prove to be quite difficult to do in practice.
That is why in this recipe we introduce auto-ARIMA, an automated approach to finding the best hyperparameters of the ARIMA class models (including variants such as ARIMAX and SARIMA).
Without going much into technical details of the algorithm, it first determines the number of differences using the KPSS test. Then, the algorithm uses a stepwise search to traverse the model space searching for a model that results in a better fit. A popular choice of evaluation metric used for comparing the models is the Akaike Information Criterion (AIC). The metric provides a trade-off between the goodness of fit of the model and its simplicity...
