vcovHAC {sandwich} | R Documentation

## Heteroskedasticity and Autocorrelation Consistent (HAC) Covariance Matrix Estimation

### Description

Heteroskedasticity and autocorrelation consistent (HAC) estimation of the covariance matrix of the coefficient estimates in a (generalized) linear regression model.

### Usage

    vcovHAC(x, ...)

    ## Default S3 method:
    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())

### 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`.
`weights` | 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.
`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 below for details.
`sandwich` | logical. Should the sandwich estimator be computed? If set to `FALSE` only the meat matrix is returned.
`ar.method` | character. The `method` argument passed to `ar` for prewhitening.
`data` | 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`.

### Details

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.

### Value

A matrix containing the covariance matrix estimate. If `diagnostics` was set to `TRUE` this has an attribute `"diagnostics"` which is a list with

`bias.correction` | multiplicative bias correction
`df` | Approximate denominator degrees of freedom

### References

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. URL http://www.jstatsoft.org/v11/i10/.

Zeileis A (2006), Object-Oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16. URL http://www.jstatsoft.org/v16/i09/.

### See Also

`weightsLumley`, `weightsAndrews`, `weave`, `kernHAC`

### Examples

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

[Package sandwich version 2.4-0 Index]