ARIMA identification


I kind of stuck here with a ARIMA estimation. I had a series which I differenced two times in order to make it stationary. The correlogram of the series looks like in the picture. There is one significant spike in the ACF, which I thought would indicate a MA(1) component and there are 3 spikes in the PACF, which could indicate an AR(3). But when I made the estimation of y=c+ar(1)+ar(2)+ar(3)+ma(1), the MA coefficient was not significant at all. I also tried various other combinations, but never got a estimation where all coefficients were significant, they should be, shouldn't they?

Also there are more spikes at the ACF of lag 24 and 25, do I need to take them into account? and if so, how could I do that?

Thanks a lot!


TS Contributor
You mean you had something like that

ar(1) sig ar(2) nsig ar(3) sig ma(1) sig

So you;re struggling to figure out if it's logical enough to use such a model. I've wonadered the same and asked 2 professors in Time Series Anlysis. Guess what? They gave a different answer. So, go figure!

Nontheless, I would go on and accept the model, I've seen it around while searching the "truth"...

Hope it helps! (I doubt about it..)
Thanks for your reply! Sorry I don't know what you mean by sig and nsig, my model was like this: y=c+ar(1)+ar(2)+ar(3)+ma(1), the problem is, I don't find a model where all coefficients are significant and which conforms more or less to the correlogram. I need to derive an ARIMA out of a restricted sub-sample. And when I first take the whole sample and find some "good" ARIMA models and try to apply them on the restricted sub-sample, some of the coefficients are not significant anymore (probably due to decreased sample size). Any ideas?


TS Contributor
That's what I mean , {sig,nsig}={significan,not significant}!

You;re trying to estimate from a fraction of your sample,say x(1):x(n) and test yor forecast on the rest series,x(n+1) throuh the end?

It's not rare to have not significant lags of order p where the p+1 lag is significantly not zero