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Hi

I am a little bit confused. I want to interpret an AR(1) Model for a financial time series and find out, whether Phi, so coefficient is equal to one (random walk), between one and zero (stationary) or equal to zero (white noise) is. not when I have a phi, but the p-value is above the significance level, can I still take the Phi value as given? this would somehow make the dicky fuller test obsolete, right? or why is there a special test to find out more about the significance of phi? And to what degree can i interpret the p-value?

If a series follows a random walk, then the AR(1) estimates are biased downward and the distribution of phi is nonstandard. Hence, the Dickey-Fuller test.

Perfect, thank you!

So that means that if we have a coefficient SERIES2(-1), a value 0.0028 but a p-value of 0.89, that means that we do indeed have to reject the null hypothesis that this is white noise? even though the coefficient phi is that low?
Thank you!

No. The Dickey-Fuller test is a test against a random walk, not white noise.

Oh sorry. Yes of course. But if one gets this result with a regular AR(1) model, since one cannot test it with the dicky fuller test.

What I mean is: if I have some data (e.g. financial time series), and I want to know more about the phi, then I use a AR(1) model. And then I have a coefficient for phi and a p-value for it. What does this p-value tell me if it is greater than 0.1?

If you mean the coefficient on the AR(1) term, or on a lagged dependent variable if you are doing it that way, then the large p-value means you cannot reject the null.

Ok now I think I got it!
We therefore cannot reject the null hypothesis that this is white noise (therefore it seems like it indeed is white noise), right?
thank you very much for your effort!

Mostly. The fact that we cannot reject that it is white noise does not mean that white noise is more likely. It may only mean that we don't have much evidence to go on.

Ok, that makes sense! Thank you very much! :-)