weightsLumley: Weighted Empirical Adaptive Variance Estimation

Description

A set of functions implementing weighted empirical adaptive variance estimation (WEAVE) as introduced by Lumley and Heagerty (1999). This is implemented as a special case of the general class of kernel-based heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimators as introduced by Andrews (1991), using a special choice of weights.

Usage

weave(x, order.by = NULL, prewhite = FALSE, C = NULL,
  method = c("truncate", "smooth"), acf = isoacf, adjust = FALSE,
  diagnostics = FALSE, sandwich = TRUE, tol = 1e-7, data = list(), ...)
weightsLumley(x, order.by = NULL, C = NULL,
  method = c("truncate", "smooth"), acf = isoacf, tol = 1e-7, data = list(), ...)

Value

weave returns the same type of object as vcovHAC

which is typically just the covariance matrix.

weightsLumley returns a vector of weights.

Arguments

x: a fitted model object.
order.by: Either a vector z or a formula with a single explanatory variable like ~ z. The observations in the model are ordered by the size of z. If set to NULL (the default) the observations are assumed to be ordered (e.g., a time series).
prewhite: logical or integer. Should the estimating functions be prewhitened? If TRUE or greater than 0 a VAR model of order as.integer(prewhite) is fitted via ar with method "ols" and demean = FALSE.
C: numeric. The cutoff constant C is by default 4 for method "truncate" and 1 for method "smooth".
method: a character specifying the method used, see details.
acf: a function that computes the autocorrelation function of a vector, by default isoacf is used.
adjust: logical. Should a finite sample adjustment be made? This amounts to multiplication with $n/(n-k)$ where $n$ is the number of observations and $k$ the number of estimated parameters.
diagnostics: logical. Should additional model diagnostics be returned? See vcovHAC for details.
sandwich: logical. Should the sandwich estimator be computed? If set to FALSE only the middle matrix is returned.
tol: numeric. Weights that exceed tol are used for computing the covariance matrix, all other weights are treated as 0.
data: an optional data frame containing the variables in the order.by model. By default the variables are taken from the environment which the function is called from.
...: currently not used.

Details

weave is a convenience interface to vcovHAC using weightsLumley: first a weights function is defined and then vcovHAC is called.

Both weighting methods are based on some estimate of the autocorrelation function $\rho$ (as computed by acf) of the residuals of the model x. The weights for the "truncate" method are

$$I\{n \rho^2 > C\}$$

and the weights for the "smooth" method are

$$\min\{1, C n \rho^2\}$$

where n is the number of observations in the model an C is the truncation constant C.

Further details can be found in Lumley & Heagerty (1999).

References

Lumley T & Heagerty P (1999). “Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.” Journal of the Royal Statistical Society B, 61, 459--477.

Examples

Run this code

x <- sin(1:100)
y <- 1 + x + rnorm(100)
fm <- lm(y ~ x)
weave(fm)
vcov(fm)

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