Feasible GLS under heteroskedasticity of unknown form (González-Coya and Perron, 2024)

Shortcut for fgls() with serial = "none". The log of the squared OLS residuals is regressed on candidate covariates z by an adaptive Lasso tuned by cross-validation; the exponentiated fit gives the weights of a weighted least-squares regression. Inference uses the sandwich of eq. (6) with the bias correction of eq. (8), so it remains valid when the skedastic model is misspecified.

Usage

lasso_fgls(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  hetero = c("lasso", "svr", "wls_s1", "wls_s2", "known", "none"),
  vcov = c("robust", "nonrobust", "HC0", "HC1", "HC2", "HC3", "bootstrap"),
  z = "auto",
  seed = NULL,
  ...
)

Arguments

formula: A model formula, as in stats::lm(). Include an intercept unless the model truly has none.
data: A data frame, a list, a ts/mts object, or a 'zoo'/'xts' object containing the variables in the formula. Rows must be in time order (unless serial = "none").
subset: Optional expression selecting rows, evaluated in data. For time series without a time index (time, or a ts/zoo data) the selected rows must be an increasing block of consecutive rows (e.g. subset = 51:200): repeated or reversed rows are an error, and so are skipped rows unless allow_gaps = TRUE.
na.action: stats::na.fail() (default) stops on missing values; stats::na.omit() or stats::na.exclude() drop them. For time series only leading and trailing missing values can be dropped. With na.exclude, residuals() and fitted() are padded with NA to the rows selected by subset, as for stats::lm().
hetero: Skedastic-function estimator: "lasso" (default), "svr", "wls_s1", "wls_s2", "known" or "none" (OLS with HC3 standard errors).
vcov: "robust" (default; eq. 8 for Lasso/SVR, eq. 7 for WLS-S1/S2, HC3 otherwise), "nonrobust", "HC0"–"HC3" or "bootstrap" (wild bootstrap).
z: Candidate covariates of the skedastic function: "auto" (default) builds \(\{x, x^2, \log x, (\log x)^2, \cos x, \cos 2x\}\) from every non-constant regressor (see make_dictionary()); a character vector of regressor names; a one-sided formula evaluated in data (e.g. ~ x + I(x^2) + w); or a numeric matrix / data frame with one row per row of data. With hetero = "wls_s1" all candidates must be strictly positive, so give them explicitly, e.g. z = "x" or z = ~ x + I(x^2) for a positive regressor x.
seed: Optional seed for the cross-validation folds and the bootstrap. The session's random number generator state is restored afterwards.
...: Further arguments passed to fgls(), e.g. variance, cv_folds, lambda_rule, weight_clip, use_t, control.

Value

An object of class "fgls"; see fgls().

References

Perron, P. and González-Coya, E. (2026). Feasible GLS for time series regression. Journal of Econometrics, 258, 106346. doi:10.1016/j.jeconom.2026.106346

González-Coya, E. and Perron, P. (2024). Estimation in the presence of heteroskedasticity of unknown form: a Lasso-based approach. Journal of Econometric Methods, 13(1), 29–48. doi:10.1515/jem-2023-0007

Romano, J. P. and Wolf, M. (2017). Resurrecting weighted least squares. Journal of Econometrics, 197(1), 1–19. doi:10.1016/j.jeconom.2016.10.003

Examples

het <- simulate_hetero(200, skedastic = "x2", seed = 1)
fit <- lasso_fgls(y ~ x, data = het, seed = 1)
fit
#> 
#> Call:
#> lasso_fgls(formula = y ~ x, data = het, seed = 1)
#> 
#> FGLS (hetero); skedastic fit: lasso (selected: x^2, log(x), cos(2x)); covariance: robust
#> 
#> Coefficients:
#> (Intercept)            x  
#>      0.9988       1.0157  
#> 
fit$skedastic$selected
#> [1] "x^2"     "log(x)"  "cos(2x)"
ols <- lasso_fgls(y ~ x, data = het, hetero = "none")
compare_fgls(OLS = ols, FGLS = fit)
#>          term statistic       OLS      FGLS
#> 1 (Intercept)  estimate 0.9492108 0.9988174
#> 2 (Intercept) std.error 0.5227244 0.4828889
#> 3 (Intercept)  ci.width 2.0490420 1.8928895
#> 4           x  estimate 1.0142749 1.0157196
#> 5           x std.error 0.2284271 0.2148521
#> 6           x  ci.width 0.8954176 0.8422049