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the second works for me because the all the coefficients have prob under 0,05

the second works for me because the all the coefficients have prob under 0,05

But my concern is if I make something wrong since when I do it with the first way the results are different and the coefficients are not significant

I'm pretty sure I know what's going on, and you're going to hate it.

ARMA uses nonlinear estimation techniques. As a general matter, you can end up in different places with different starting values. That's almost certainly what's going on.

But wait! It gets worse! Your model appears to be overspecified. You have what's called "near root cancellation." Loosely speaking, you're finding equal AR and MA coefficients that simply cancel one another. Unfortunately, under these circumstances the t-statistics and p-values are meaningless.

Try a model with just a couple of ARMA terms and you'll probably find the log likelihood is about the same.

So there is no way to overcome this overspecification? I mean this sample is useless? Any ideas of how to modify it?

I don't know what you're trying to accomplish. Why not start with just an AR(1) and see if that works well enough for your purposes.

Actually, It looks like we've slipped up on this one.

There's some code that determines whether backcasting can be used for calculating the pre-sample innovations based on whether the MA coefficients appear to be stable for backcasting, and it's not quite right when you're reordering the MA terms. That's what is making the reordered specification estimate slightly differently (and why the specifications estimate the same if MA backcasting is off). We'll fix this in our next patch.

By the way, there are still a lot of issues with the specification. If you use 'View...ARMA Structure... Roots' from the estimated equation you'll see that the AR and MA roots seem to be pretty much right on top of eachother. This is not what you want to see in a healthy specification.

Actually, It looks like we've slipped up on this one.

There's some code that determines whether backcasting can be used for calculating the pre-sample innovations based on whether the MA coefficients appear to be stable for backcasting, and it's not quite right when you're reordering the MA terms. That's what is making the reordered specification estimate slightly differently (and why the specifications estimate the same if MA backcasting is off). We'll fix this in our next patch.

By the way, there are still a lot of issues with the specification. If you use 'View...ARMA Structure... Roots' from the estimated equation you'll see that the AR and MA roots seem to be pretty much right on top of eachother. This is not what you want to see in a healthy specification.

What Chris is saying is that once the patch is done, you'll probably get the same meaningless estimate no matter what the order of the specification.

In any event, your data appears not to be serially correlated. That suggests that an ARMA model is not appropriate. There does appear to be some autocorrelation at lag 9, but unless there is an explanation for that I suspect it's mostly random.

I don't know what you're trying to accomplish. Why not start with just an AR(1) and see if that works well enough for your purposes.

The series is rate returns of usd/eur and i want to forecast the outofsamle. The insample are the first 1781 values and the outofsample the rest 514 (of the 2295 whole sample) and I have to do this with ARMA model. Or find the optimal one.

Regarding the extra reply u made, to summarize the right structure is the one that starts from the smaller to the bigger. Thus AR(1) AR(2) is correct and AR(2) AR(1) is not quite right.

If as you said t statistic kai p probabilities dont have a meaning in an overspecified sample, should I try to find a combination of ar, ma regardless of the probabilities?

Thanx for all the help!

Oh. Returns on exchange rates are extremely hard to predict. This is, more or less, a result of efficient markets. You are unlikely to be able to predict by much more than the sample average. You might be able to get somewhat better prediction using other variables, such as forward rates and interest rates.