spectrum0.mvar {ergm}

Multivariate version of coda's spectrum0.ar().

Description

Its return value, divided by nrow(cbind(x)), is the estimated variance-covariance matrix of the sampling distribution of the mean of x if x is a multivatriate time series with AR(p) structure, with p determined by AIC.

Usage

spectrum0.mvar(
  x,
  order.max = NULL,
  aic = is.null(order.max),
  tol = .Machine$double.eps^0.5,
  ...
)

Arguments

x

a matrix with observations in rows and variables in columns.

order.max

maximum (or fixed) order for the AR model.

aic

use AIC to select the order (up to order.max).

tol

drop components until the reciprocal condition number of the transformed variance-covariance matrix is greater than this.

...

additional arguments to ar().

Value

A square matrix with dimension equalling to the number of columns of x, with an additional attribute "infl" giving the factor by which the effective sample size is reduced due to autocorrelation, according to the Vats, Flegal, and Jones (2015) estimate for ESS.

Note

ar() fails if crossprod(x) is singular, which is remedied by mapping the variables onto the principal components of x, dropping redundant dimentions.