weightsAndrews: Kernel-based HAC Covariance Matrix Estimation

Description

A set of functions implementing a class of kernel-based heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators as introduced by Andrews (1991).

Usage

kernHAC(x, order.by = NULL, prewhite = 1, bw = NULL,
  kernel = c("Quadratic Spectral", "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"),
  approx = c("AR(1)", "ARMA(1,1)"), diagnostics = FALSE, sandwich = TRUE, data = list(), ...)
weightsAndrews(x, order.by = NULL, bw = NULL,
  kernel = c("Quadratic Spectral", "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"),
  prewhite = 1, data = list(), ...)
bwAndrews(x, order.by = NULL, kernel = c("Quadratic Spectral", "Truncated",
  "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)", "ARMA(1,1)"),
  weights = NULL, prewhite = 1, data = list())

Arguments

a fitted model object of class "lm" or "glm".

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 assum

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 = F

numeric. The bandwidth of the kernel (corresponds to the truncation lag). If set to NULL (the default) it is adaptively chosen by the function bwAndrews.

kernel

a character specifying the kernel used. All kernels used are described in Andrews (1991).

approx

a character specifying the approximation method if the bandwidth bw has to be chosen by bwAndrews.

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.

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.

...

further arguments passed to bwAndrews.

weights

numeric. A vector of weights used for weighting the estimated coefficients of the approximation model (as specified by approx). By default all weights are 1 except that for the intercept term (if there is more than one variable).

Value

kernHAC returns the same type of object as vcovHAC which is typically just the covariance matrix.
weightsAndrews returns a vector of weights.
bwAndrews returns the selected bandwidth parameter.

Details

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

The kernel weights underlying weightsAndrews are directly accessible via the function kweights and require the specification of the bandwidth parameter bw. If this is not specified it can be chosen adaptively by the function bwAndrews (except for the "Truncated" kernel). The automatic bandwidth selection is based on an approximation of the estimating functions by either AR(1) or ARMA(1,1) processes. To aggregate the estimated parameters from these approximations a weighted sum is used. The weights in this aggregation are by default all equal to 1 except that corresponding to the intercept term which is set to 0 (unless there is no other variable in the model) making the covariance matrix scale invariant.

Further details can be found in Andrews (1991).

The estimator of Newey & West (1987) can be obtained using the "Bartlett" kernel.

References

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817--858.

Newey WK & West KD (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55, 703--708.

Examples

Run this code

curve(kweights(x, kernel = "Quadratic", normalize = TRUE),
      from = 0, to = 3.2, xlab = "x", ylab = "k(x)")
curve(kweights(x, kernel = "Bartlett", normalize = TRUE),
      from = 0, to = 3.2, col = 2, add = TRUE)
curve(kweights(x, kernel = "Parzen", normalize = TRUE),
      from = 0, to = 3.2, col = 3, add = TRUE)
curve(kweights(x, kernel = "Tukey", normalize = TRUE),
      from = 0, to = 3.2, col = 4, add = TRUE)
curve(kweights(x, kernel = "Truncated", normalize = TRUE),
      from = 0, to = 3.2, col = 5, add = TRUE)

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

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