I think I will start by looking at AR.
I am reading that in order to fit an AR model, the data-series must be stationary. This means that the mean, variance, autocorrelation etc. do not vary in time. As you can imagine, if this is the case then making predictions is far simpler. The data can be said to be stationary if there is a unit-root, which can be tested using the Dickey-Fuller test. In order that the data be stationary (if it isn't already and as it probably wont be with raw financial data), it has to be stationarized which has to be done through the use of mathematical transformations (don't worry it can be easier than it sounds).
The above is not quite right;
- there are many kinds of non-stationarity (non-stationarity merely means that the probability distribution of the series is not translation-invariant, nothing more)
- one very particular example (quite mild, too) of non-stationary time-series (one of infinitely many) would be I(1) time-series, i.e., integrated of order one (having a unit root); a.k.a. unit-root, a.k.a. difference-stationary -- because the first difference is stationary (this is why this case is so mild: in general you can't be sure you can do anything to make a non-stationary process stationary),
- the tests mentioned here, so-called "unit root tests", are for this very particular example of non-stationarity (and only for this very particular example of non-stationarity), nothing more,
- unit root tests include DF (1976), ADF (1979), PP (1988) (and dozens more),
- the original Dickey–Fuller (DF) test is not asymptotically valid if there's serial correlation present in the error terms (it doesn't allow for serial correlation in the first differences),
- augmented Dickey–Fuller test (ADF) fixes the above,
- as for Phillips–Perron (PP): "there is now a good deal of evidence that PP tests perform less well in finite samples than ADF tests" (Davidson and MacKinnon, "Econometric Theory and Methods"), so you might as well ignore it,
- you might also consider KPSS -- while the above tests are to test for unit root as the null hypothesis (H0), KPSS has it as the alternative hypothesis (H1).
It's best not to use
general-case-name and
rare-and-special-case-name (like
non-stationary and
I(1)/with-unit-root/difference-stationary) terms interchangeably
Also avoid the related derived terms -- I probably wouldn't say "stationarized", since in general there's nothing you can do to non-stationary time-series to make them stationary (well, other than applying somewhat lossy transformations, like multiplying everything by zero ;]); again, if you're dealing with the special case of I(1)/difference-stationary then say so, and then it becomes obvious what to do with difference-stationary time-series, right?