Multiple seasonal time-series : interpret tbats.components() function results in R

Question

I'm using the TBATS model of the forecast package with Google Analytics data, to forecast web trafic containing multiseasonal effects (msts).

I have two year of daily data that contains two columns like these :

date           sessions
2015-01-01     2667
2015-01-02     3542
2015-01-03     2383
2015-01-04     2772
2015-01-05     7797
2015-01-06     7599

I made one forecast for all my data and another forecast with data containing only a segment of users.

In the first case (all data), I obtained this result :

And in the second case (segment data), I obtained this :

My questions :

1. How to interpret the slope component? I get it in the first case but not in the second. Is there a reason for that?
2. What could do that the Lo/Hi points are so much wider in the second case?

Answer 1

In your first example two years of annual data was used with no apparent effects due to omitted variables like price , promotion etc or level shifts . The two years of forecasts are visually identical with presumptive symmetric forecasting confidence limits totally ignoring any unusual activity in the future. Your second example based upon only 1 year of data has less predictability (fitting statistics ... smaller r-square ...larger error variance) thus wider limits would be expected as no seasonal component was identifiable due to only 1 year of data.