## Compute correlogram for angular and linear descriptors of a movement path

### Description

The functions `acfdist.ltraj` and `acfang.ltraj` compute (and by default plot) a correlogram-like function .

### Usage

```acfdist.ltraj(x, which = c("dist", "dx", "dy"), nrep = 999, lag = 1,
plot = TRUE, xlab = "Lag", ylab = "autocorrelation")

acfang.ltraj(x, which = c("absolute", "relative"), nrep = 999, lag = 1,
plot = TRUE, xlab = "Lag", ylab = "autocorrelation")
```

### Arguments

 `x` an object of the class `ltraj` `which` to select on which parameter the autocorrelation should be computed (see details). `nrep` the number of repetitions used to test the significance of autocorrelation for each lag value. `lag` maximum lag at which to calculate the autocorrelation. Default is 1. `plot` logical. If 'TRUE' (the default) the autocorrelation is plotted. `xlab` a title for the x axis `ylab` a title for the y axis

### Details

The function `acfdist.ltraj` is used to compute a correlogram for linear descriptors and `acfang.ltraj` for angular descriptors (see `as.ltraj` for a description of these descriptors).

Statistics used are defined in Dray et al. (in press). They are based on squared differences between successive values. For angular descriptors, the statistic is based on the chord distance.

In the case of missing data, the computation of the correlograms is restricted to the pairs of successive observed data and only observed data are permuted (i.e. the structure of the missing data is kept constant under permutation).

The grey area represents a 95 % interval obtained after permutation of the data. If the observed data is outside this region, it is considered as significant and represetend by a black symbol. Note that no multiple-comparison adjustement is performed.

### Value

A list of matrices. Each matrix corresponds to a 'burst'. The matrix contains for each lag value (column), the values of autocorrelation (observed, and the 2.5 %, 50 % and 97.5 % quantiles of for the set of `nrep` permutations of values).

### Author(s)

Stephane Dray dray@biomserv.univ-lyon1.fr

### References

Dray, S., Royer-Carenzi, M. and Calenge, C. The exploratory analysis of autocorrelation in animal movement studies. Ecological Research, in press.

Calenge, C., Dray, S. and Royer-Carenzi, M. (2009) The concept of animals trajectories from a data analysis perspective. Ecological Informatics, 4,34–41.

`as.ltraj` for additional information on the class `ltraj`, `wawotest` for a simple test of the autocorrelation of the descriptive parameters on the trajectory.

### Examples

```## Not run:
data(puechcirc)
puechcirc
acfang.ltraj(puechcirc, lag=5)
acfdist.ltraj(puechcirc, lag=5)

## End(Not run)
```