I've been working on my own question and I can report the following results after trying all 3 options to the series in question. I've done a baseline model that just includes the regressor variable and tried the three approaches to this with the following validation:
- The models are all tested with the same parameters in a ARIMAX model.
- The test includes a walk-forward validation of 5 periods of 30 days each in the "after covid period"
The baseline model has a 19.88% MAPE over the 5 periods.
1. Use a Step regressor during the shutdown period.
I've introduced a variable into the model with a value of 1 during the shutdown period and 0 elsewhere. This was fairly easy to implement
df['shutdown'] = (df.index > pd.to_datetime('2020-03-06')) & (df.index < pd.to_datetime('2020-06-12')) == 1
I added this variable to the model and made an interaction with the other regressors and added it to my ARIMA model.
This approach yielded a 21.52% average MAPE over 5 periods in the walk forward validation.
It was also tested to add the regressor independently but the error was higher than the one initially tested.
2. Remove the period entirely and consider that it 'never happened'.
This approach was done by removing the shutdown period entirely and training the data where each observation had occurred a few months earlier, and then converting back to the original dates, of course this was also done for the regressor variables as well.
This yielded a result of 19.88% average MAPE over 5 periods in the walk forward validation, a fairly big performance improvement comparing it to the baseline model.
3. Adjusting the shutdown period to match the magnitude of pre-covid data.
To do this the series was adjusted with a multiplicator to reach the pre-covid levels. This was the worst of the options, because the scale and relation between the regressors and the dependent variable was lost. It didn't make sense to validate this model with the stepforward validation.
After all of this, a different approach was intended:
4. Adding COVID-19 information to the model: Number of active daily cases.
I got the data from Our World in Data COVID Datasetand after cleaning the series and smoothing it, I added the regressor with number of daily active cases to the model.
This yielded a result of 13.56% average MAPE over 5 periods in the walk forward validation, being this the best result and trimming a whole 6 percentage points from the error.
The conclusion here is that, at least in this case, there was a variable that was explaining the behavior both in the shotdown period and afterwards, and this provided the best result.