weightsLumley {sandwich} R Documentation

## Weighted Empirical Adaptive Variance 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

```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(), ...)
```

### Arguments

 `x` 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 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"` und 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 r (as computed by `acf`) of the residuals of the model `x`. The weights for the `"truncate"` method are

I{n * r ** 2 > C}

and the weights for the `"smooth"` method are

min{1, C * n * r ** 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).

### Value

`weave` returns the same type of object as `vcovHAC` which is typically just the covariance matrix.
`weightsLumley` returns a vector of weights.

### References

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

`vcovHAC`, `weightsAndrews`, `kernHAC`
```x <- sin(1:100)