spectrum0.mvar: Multivariate version of 'coda"s 'spectrum0.ar()'.

In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

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	tolerance used in detecting multicollinearity. See Note below.
...	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. This is is remedied as follows:

1. Standardize the variables.

2. Use the eigenvectors to map the variables onto their principal components.

3. Use the eigenvalues to standardize the principal components.

4. Drop those components whose standard deviation differs from 1 by more than tol. This should filter out redundant components or those too numerically unstable.

5. Call ar() and calculate the variance.

6. Reverse the mapping in steps 1-4 to obtain the variance of the original data.

ergm documentation built on Oct. 7, 2024, 5:08 p.m.