Heteroscedasticity and autocorrelation consistent (HAC) estimation of the covariance matrix of the coefficient estimates in a (generalized) linear regression model.
vcovHAC(x, ...)# S3 method for default
vcovHAC(x, order.by = NULL, prewhite = FALSE, weights = weightsAndrews,
adjust = TRUE, diagnostics = FALSE, sandwich = TRUE, ar.method = "ols",
data = list(), ...)
meatHAC(x, order.by = NULL, prewhite = FALSE, weights = weightsAndrews,
adjust = TRUE, diagnostics = FALSE, ar.method = "ols", data = list(), ...)
A matrix containing the covariance matrix estimate. If diagnostics
was set to TRUE this has an attribute "diagnostics" which is a list
with
multiplicative bias correction
Approximate denominator degrees of freedom
a fitted model object.
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).
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.
Either a vector of weights for the autocovariances or a
function to compute these weights based on x, order.by,
prewhite, ar.method and data. If weights
is a function it has to take these arguments. See also details.
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.
logical. Should additional model diagnostics be returned? See below for details.
logical. Should the sandwich estimator be computed?
If set to FALSE only the meat matrix is returned.
character. The method argument passed to
ar for prewhitening.
an optional data frame containing the variables in the order.by
model. By default the variables are taken from the environment which
vcovHAC is called from.
arguments passed to sandwich (in vcovHAC)
and estfun (in meatHAC), respectively.
The function meatHAC is the real work horse for estimating
the meat of HAC sandwich estimators -- the default vcovHAC method
is a wrapper calling
sandwich and bread. See Zeileis (2006) for
more implementation details. The theoretical background, exemplified
for the linear regression model, is described in Zeileis (2004).
Both functions construct weighted information sandwich variance estimators
for parametric models fitted to time series data. These are basically
constructed from weighted sums of autocovariances of the estimating functions
(as extracted by estfun). The crucial step is the specification
of weights: the user can either supply vcovHAC with some vector of
weights or with a function that computes these weights adaptively (based on
the arguments x, order.by, prewhite and data).
Two functions for adaptively choosing weights are implemented in
weightsAndrews implementing the results of Andrews (1991) and
in weightsLumley implementing the results of Lumley (1999).
The functions kernHAC and weave respectively
are to more convenient interfaces for vcovHAC with these functions.
Prewhitening based on VAR approximations is described as suggested in Andrews & Monahan (1992).
The covariance matrix estimators have been improved by the addition of a bias correction and an approximate denominator degrees of freedom for test and confidence interval construction. See Lumley & Heagerty (1999) for details.
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica, 59, 817--858.
Andrews DWK & Monahan JC (1992). “An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator.” Econometrica, 60, 953--966.
Lumley T & Heagerty P (1999). “Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.” Journal of the Royal Statistical Society B, 61, 459--477.
Newey WK & West KD (1987). “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703--708.
Zeileis A (2004). “Econometric Computing with HC and HAC Covariance Matrix Estimators.” Journal of Statistical Software, 11(10), 1--17. tools:::Rd_expr_doi("10.18637/jss.v011.i10")
Zeileis A (2006). “Object-Oriented Computation of Sandwich Estimators.” Journal of Statistical Software, 16(9), 1--16. tools:::Rd_expr_doi("10.18637/jss.v016.i09")
weightsLumley, weightsAndrews,
weave, kernHAC
x <- sin(1:100)
y <- 1 + x + rnorm(100)
fm <- lm(y ~ x)
vcovHAC(fm)
vcov(fm)
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