ARIMA is unstable on incomplete seasons #50
Description
I am making ARIMA predictions with yearly seasonality and data. with 24 months of history, the prediction is as good as cn be expected with s little data, but if I use 25 months of history, the prediction is very unstable (slightly modifying one measure can result in a massive trend change).
Example input : 10 | 11 | 12 | 8 | 6 | 4 | 5 | 6 | 6 | 5 | 4 | 3 | 2 | 2.5 | 3 | 2 | 1 | 0.5 | 0.1 | 0 | 1 | 0.2 | 1 | 0 | 0.3 | 0.4 | 0.2
with the following ARIMA parameters :
p = 0
d = 1
q = 1
aP = 0
aD = 1
aQ = 1,
the previsions are increasing (athough the history is clearly decreasing). Changing the second value (the 11) into a 13 or a 9 makes the predictions seem correct.
When I perform the same prediction with only the 24 first value, the prediction is not as sensitive, and changing one input value only marginally affects the prediction.
See screenshot :
I suspect this is due to this line in ArimaModel.java :
this.differencedSeries = observations.difference(1, order.d()).difference(seasonalFrequency, order.D());