NHMSAR (version 1.0)

cross.cor.MSAR: empirical cross-correlation for multivariate MSAR time series

Description

cross.cor.MSAR computes the cross-correlation between two components. The cross-corelation can be estimted for the whole time series or regime by regime.

Usage

cross.cor.MSAR(data, X=NULL, nc1 = 1, nc2 = 2, lag = 10, regime = 0, CI = FALSE, 
  Bsim = 0, N.samples = 1, add = FALSE, col = 1, names = NULL, alpha = 0.1)

Arguments

data

observed (or reference) time series, array of dimension T*N.samples*d

X

time series of regimes associated to data

nc1

first component to be considered

nc2

second component to be considered

lag

maximum lag (default=10). The cross-correlation is estimated for lags -lag:lag.

regime

has to be an integer between 0 and M, with M the number of regimes. If regime=0, the cross correlaiton is computed for the whole time series. If regime=m>0, the corss corelation is computed considereing only the sub-sequences in regime m.

CI

If CI=TRUE fluctuation intervals are computed, default is FALSE

Bsim

useful for computation of confidence intervals. When observed and simulated data are compared, one expects that the number of simulated time series is Bsim*N.samples

N.samples

useful for computation of confidence intervals. N.sample describes the number of independant time series in the observed (or reference) data

add

if add=TRUE the empirical cross-correlation is added to the current plot.

col

color of the line

names

list with the names of components of data

alpha

level for the computation of the fluctuation intervals. default=0.1

Value

• returns a list including:
• ..$ccf
  empirical cross-correlation
• ..$lag
  abscissa for the cross-correlation
• ..$CI
  fluctuation intervals

Details

The cross-correlation functions are computed from one or several independent realizations of the same length.

References

Bessac, J., Ailliot, P., & Monbet, V. (2013). Gaussian linear state-space model for wind fields in the North-East Atlantic. arXiv preprint arXiv:1312.5530.

See Also

cor.MSAR, cor, valid_all

Examples

data(Wind)
T = dim(U)[1]
c = cross.cor.MSAR(U,nc1=1,nc2=18,names=1:18)
## Not run
#Y = U[,,c(1,18)]
#theta.init=init.theta.MSAR(Y,M=2,order=2,label="HH")
#res.hh = fit.MSAR(Y,theta.init,verbose=TRUE,MaxIter=200)
#Bsim = 20
#N.samples = dim(U)[2]
#Ksim = Bsim*N.samples
#Y0 = Y0
#Y.sim = simule.nh.MSAR(res.hh$theta,Y0 = Y0,T,N.samples = Ksim) 
#c.sim = cross.cor.MSAR(Y.sim$Y,nc1=1,nc2=2,names=c(1,18),
#   CI=TRUE,Bsim=Bsim,N.samples=N.samples,add=TRUE,col="red")