I Have a variable (time series) which is nonstationary. I found that from the graph which seems to have a stochastic trend and the correlogram has a typical nonstationary pattern. After that, I've been asked to find the parsimonious ARMA model (using information criteria), and by following the Box-Jenkins methodology, go down till forecasting. Notice that at this point, I havent been asked to make a unit root test to check if the series is stationary or not...

Is it possible a nonstationary series to produce a stationary ARMA model, which will give us reliable forecasting?

After the forecasting, they ask me to make a unit root test (where of course I find that the variable is non stationary). As a next step I take the variable in 1st differences, and follow the same procedure to find an ARMA model with best information criteria. I also make some comparissons with the model that I found at the 1st step, but after that they dont ask me to follow the Box-Jenkins methodology again and make a forecast from the ARMA model produced by the differenced variable...

So what I’m confused about is:

Why did they ask me to find an ARMA from a non stationary variable? Can a nonstat. Variable produce stationary ARMA model and reliable forecasting?

Wouldn’t it be normal to ask me to follow the Box Jenkins methodology in the second model (where the variable is differenced) and make a forecast from there?

Any answer would be helpful!

  • $\begingroup$ Without seeing the data, your reasoning is okay, if the series is not stationary and taking first differences renders it stationary you should do that. Be aware that a series may be or look non-stationary due to issues other than a stochastic trend, e.g. deterministic trend or level shift. Maybe you are asked to fit both models to compare the results and see the effect of ignoring the presence of a unit root (you may compare the model that is chosen, parameter estimates, standard errors, forecasts). $\endgroup$ – javlacalle Jul 24 '14 at 7:24
  • $\begingroup$ btw the ARMA model that I found (from the time series in levels) the sum of the coefficients on AR components are less than 1, and from the corrrelogram of the residuals shows that they are not autocorrelated.. so the question still remains: is it possible to construct a stationary ARMA model from a nonstationary series? ( from the results above looks stationary!). Is the forecast reliable? and why didnt they ask me to produce an ARMA model from the variable in 1st differences in the first place? and make the forecast from there... $\endgroup$ – Tony Jul 25 '14 at 4:21

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