# Re: [R] Question concerning "pastecs" package

From: Philippe Grosjean <phgrosjean_at_sciviews.org>
Date: Fri, 25 May 2007 11:00:01 +0200

Hello,

?turnpoints

Regarding your specific question, 'info' is the quantity of information I associated with the turning points:

I = -log2 P(t)

where P is the probability to observe a turning point at time t under the null hypothesis that the time series is purely random, and thus, the distribution of turning points follows a normal distribution with:

E(p) = 2/3*(n-2)
var(p) = (16*n - 29)/90

with p, the number of observed turning points and n the number of observations. Ibanez (1982, in French, sorry... not my fault!) demonstrated that P(t) is:

P(t) = 2*(1/n(t-1)! * (n-1)!)

As you can easily imagine, from this point on, it is straightforward to construct a test to determine if the series is random (regarding the distribution of the turning points), more or less monotonic (more or less turning points than expected), See also the ref cited in the online help (Kendall 1976).

References:

Ibanez, F., 1982. Sur une nouvelle application de la théorie de l'information à la description des séries chronologiques planctoniques. J. Exp. Mar. Biol. Ecol., 4:619-632

Kendall, M.G., 1976. Time-series, 2nd ed. Charles Griffin & Co, London

Best,

Philippe Grosjean

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( ( ( ( ( Prof. Philippe Grosjean
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( ( ( ( ( Numerical Ecology of Aquatic Systems   ) ) ) ) ) Mons-Hainaut University, Belgium ( ( ( ( (

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Rainer M. Krug wrote:

```> Hi
>
> I just installed the pastecs package and I am wondering: is there an
> english (or german) translation of the file pastecs.pdf? If not, is
> there an explanation somewhere of the object of type 'turnpoints' as a
> result of turnpoints(), especially the "info" field?
>
> Thanks,
>
> Rainer
>

______________________________________________
```
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