Candidate covariates for the skedastic function

Builds the default dictionary of candidate covariates used by fgls() and lasso_fgls() with z = "auto": for every non-constant regressor \(x\), the columns \(x\), \(x^2\), \(\log x\) and \((\log x)^2\) (only when \(x > 0\)), \(\cos x\) and \(\cos 2x\). This contains the specification \(z = (1, x, [\log x]^2, x^2, \cos x, \cos 2x)\) of the simulations of González-Coya and Perron (2024); the intercept of the skedastic regression is always included and never penalized. Binary (dummy) columns are passed through untransformed, undefined or constant transforms are skipped and duplicated columns are removed.

Usage

make_dictionary(
  x,
  transforms = c("linear", "poly2", "log", "trig"),
  skip = NULL
)

Arguments

x

A numeric matrix or data frame of regressors (constant columns are ignored), or a numeric vector.

transforms

Transform families: "linear" (\(x\)), "poly2" (\(x^2\)), "log" (\(\log x\), \((\log x)^2\) for positive \(x\)) and "trig" (\(\cos x\), \(\cos 2x\)).

skip

Columns (names or positions) to leave out, e.g. lagged dependent variables.

Value

A numeric matrix with one column per candidate covariate and informative column names.

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

See also

Other heteroskedasticity: lasso_fgls()

Examples

X <- cbind(const = 1, x = seq(1, 4, length.out = 10), d = rep(0:1, 5))
colnames(make_dictionary(X))
#> [1] "x"        "x^2"      "log(x)"   "log(x)^2" "cos(x)"   "cos(2x)"  "d"       
colnames(make_dictionary(X, transforms = c("linear", "poly2")))
#> [1] "x"   "x^2" "d"