The total impact of a month is different from the difference between the predicted value of that month and the predicted value of the previous month

[ahbon123]

Hello ChadFulton,

Thank you for your statespace_large_dynamic_factor_models tutorial: http://www.chadfulton.com/topics/statespace_large_dynamic_factor_models.html

First, let's look at the changes in the forecast for the second quarter of 2020:

2020-02 forecast for real GDP growth in 2020Q2: 2.68%
2020-03 forecast for real GDP growth in 2020Q2: 2.52% # decrease 0.16 pct
2020-04 forecast for real GDP growth in 2020Q2: -8.23% # decrease 10.75 pct
2020-05 forecast for real GDP growth in 2020Q2: -37.17% # decrease 28.94 pct
2020-06 forecast for real GDP growth in 2020Q2: -22.33% # increase 14.84 pct

Second, let's look at the Total impact on 2020Q2 forecast:

# Print the table of impacts from data in each group,
# along with a row with the "Total" impact
(group_impacts.T
.append(group_impacts.sum(axis=1).rename('Total impact on 2020Q2 forecast'))
.round(2).iloc[:, 1:])

Out:

group 2020-03 2020-04 2020-05 2020-06
...
Total impact on 2020Q2 forecast -0.16 -10.70 -29.30 17.18

We can see that the total impact on 2020Q2 forecast for 2020-03 is equal to the forecast value of actual GDP for 2020-03 minus the forecast value of actual GDP for 2020-02, but there are different degrees of difference in other months.

My question is: what is the reason for this difference? Normally, should the total impact of a certain month on the 2020Q2 forecast be equal to the difference between the forecast value of this month and the forecast value of the previous month?