Just curious as to the present state of the art for testing stationarity other than ADF test. Would be glad to get your input in this regard.

Arnab,

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-stationarity.

I hope this helps.

Regards

Aidan

I suggest that second order differencing be done and an arima(p,2,q) model be fitted and compared with the R-fitted arima(1,1,0) model.

May I suggest you try fractional differencing first before you proceed to implement first/second order differencing.

What about the justification of non significant correlations in the acf and pacf of the 1st difference data?