I've got some time-series business data that I can fit relatively well with a
ARIMA(2,1,0)(1,1,0) model (using R's excellent
forecast::Arima -- thanks Prof. Hyndman!). The series is dominated by seasonal effects, but has trends as well, thus the differencing. I'm not an expert in forecasting.
I'm exploring a future experiment (power analysis sorts of things) by simulating the effect of some sort of intervention that may increase (or decrease) the values in the series, probably multiplicatively. To do this, I'm scaling the numbers for the last N months by X%, and using the
xreg parameter to change the model from a differenced AR(1) to a regression with time-series errors. The vector I'm using as the regressor looks like
[0, 0, ..., 0, 1, 1, 1], where 1s represent the months with the intervention in effect.
The coefficient I get from the model appears to be an additive effect, which makes sense, but is much smaller than the actual effect (4000 vs 100,000). However, when I use
forecast, with and without 1s in the regressor, the difference is of the expected magnitude -- if anything, too high.
So, my questions:
- How do I interpret that coefficient. Is it additive?
- Is it correct to use 1s in the regressor vector for all time periods that the treatment is in effect, or should I be thinking of this as an impulse that offsets the trend in the ARIMA model, and using a pattern like
0, 1, 0, 0, -1, 0?
- Any other advice?
This is related to these questions, which either don't answer my question or I don't fully understand:
- Variables importance on regression with ARIMA errors model
- Intervention analysis in time-series regression with seasonal ARIMA errors
- How to detect a significant change in time series data due to a "policy" change?