I am currently studying ARIMA models. When I checked for a python library to train one, I stumbled upon statsmodels which features ARIMA (and SARIMAX from which ARIMA inherits). However, there is one thing I'm not quite sure to understand.

When differenciating, we account for a trend in the time serie. Nevertheless, we can still specify a deterministic trend in the model argument.

From what I understood, setting a deterministic trend will:

• result in more accurate forecasts thanks to a fixed variance
• not be able to adjust if the trend changes. For instance if a metric goes from growing up rapidly to having a slight slope, the model with the deterministic trend will continue with the same slope.

what are the differences between the two options?

Is there a use case where it would be useful to put both a trend and a integral order?

thank you in advance for your time.

I am currently studying ARIMA models. When I checked for a Python library to train one, I stumbled upon statsmodels which features ARIMA (and SARIMAX from which ARIMA inherits). However, there is one thing I'm not quite sure I understand.

When differencing, we account for a trend in the time series. Nevertheless, we can still specify a deterministic trend in the model argument.

From what I understood, setting a deterministic trend will:

• result in more accurate forecasts thanks to a fixed variance
• not be able to adjust if the trend changes. For instance if a metric goes from growing up rapidly to having a slight slope, the model with the deterministic trend will continue with the same slope.

What are the differences between the two options?

Is there a use case where it would be useful to put both a trend and a integral order?