Table 2 Steps taken to model and predict data using VARMAX and VECM methods

1) Apply logarithmic transformation to the data, to guarantee that all forecasts are positive;

2) Apply differencing of 7 to remove seasonality \(z_{t} = y_{t} - y_{t} - 7\);

2) Train VAR model to choose lag order with AIC;

3) Apply differencing of 1 to remove trend (if needed) \(z_{t} = yt - y_{t} - 1\);

3) Select cointegration rank, using the Johansen Cointegration test;

4) Train model (60% of data) and choose lag order based on AIC

4) Train VECM model with the selected lag order and cointegration rank using train set (60% of data);

5) Test best model (lowest AIC) using the test set (40% of data);

5) Test model using the test set (40% of data);

6) Test the best model (lowest AIC) using the test set (20% of the data)