Question

For a given problem both the ACF and the PACF of the different data show a single significanr spikenay lag 1. the two potential models are:

ARIMA (1,1,0)

ARIMA (0,1,1)

I dont understand why for ARIMA (p,d,q) the "d" is 1. could you please explain?

Answer 1

Stationarity tests can have low power and sometimes give false positives, especially when you over-difference. I always follow two approaches:

- The first is simply graphical. Plot the series and see what it looks like. From the description of your data (accidental death), while I could imagine it being of Order 1, I find it hard to imagine that it is of Order 2 (i.e. the first difference is of Order 1). Does the first difference 'look' non-stationary? Volatility in the autocorrelogram of the second difference series is also an indication over-differencing.

- The second, more formal, approach is to run alternative tests. In particular, I recommend the KPSS test which (unlike the Dickey-Fuller and most other tests) has the null hypothesis that the series is stationary. Normally when you have over-differenced, you will find that the KPSS accepts stationarity even if the ADF (or other tests) suggest non-stationari