[R] Stationarity of a Time Series

David Jones daj at ceh.ac.uk
Wed Jan 23 11:48:22 CET 2008

Prof Brian Ripley wrote:
> On Tue, 22 Jan 2008, Pfaff, Bernhard Dr. wrote:
>> Hello Stephen,
>> stationarity tests as well as unit root tests have been implemented
>> in a couple of packages. For instance, as already mentioned:
>> tseries, but 
>> also uroot, fUnitRoots and urca. See the annotated task view
>> "Econemtrics" and "Finance" for further information.
> But note that these tests apply to just a few ways in which a series
> might be non-stationary: they all seem an econmetrician's view of
> possible non-stationarity.
> In the end stationarity is a modelling assumption: it depends on what
> might have happened but did not.  E.g. a sine wave process is
> stationary if and only if it has a random (uniform) phase, and you
> cannot tell that from a single realization.
> 'Anna Karenina applies'[*] (as to most pure significance tests).
> [*] Google it if you need elucidation.

Apart from the "drift" type of nonstationarity, other types would be ..
(i) seasonality;
(ii) local changes in mean-level;
(iii) local changes in correlation;
(iv) local changes in variability.
Some of these might be made formally stationary as above.

David Jones

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