# Multivariate Jacobian Index Estimated From a Multivariate Autocorrelation Matrix

Source:`R/multiAR.R`

`multiAR.Rd`

Estimate the dominant Jacobian eigenvalue of a multivariate time series using autocorrelated stochastic differential equations

## Source

Williamson and Lenton (2015). Detection of bifurcations in noisy coupled systems from multiple time series. Chaos, 25, 036407

## Arguments

- data
Numeric matrix with time in first column and species abundance in the remainder.

- scale
Boolean. Should data be scaled prior to estimating the Jacobian.

- winsize
Numeric. Defines the window size of the rolling window as a percentage of the time series length.

- p
Numeric. Defines the model order. Defaults to `1`.

- dt
Numeric An appropriate time step

## Value

A dataframe where the first column is last time index of the window and the second column is the estimated index value. A value <1.0 indicates stability, a value >1.0 indicates instability.

## Examples

```
#Load the multivariate simulated
#dataset `simTransComms`
data(simTransComms)
#Subset the second community prior to the transition
pre_simTransComms <- subset(simTransComms$community2,time < inflection_pt)
#Estimate the univariate stability index for the first species in
#the second community
egarJ <- multiAR(data = pre_simTransComms[,2:7],
winsize = 25, dt = 1)
```