fgls
Feasible GLS for Serial Correlation and Heteroskedasticity
Feasible generalized least squares (FGLS) estimators for linear
regressions whose errors are serially correlated, heteroskedastic of
unknown form, or both. Serial correlation is handled by the
autoregressive filter of Perron and González-Coya (2026)
fgls
fgls estimates linear regressions by feasible generalized least squares when the errors are serially correlated, heteroskedastic of unknown form, or both:
- Serial correlation (Perron and González-Coya, 2026). An AR filter is estimated from a Durbin regression, with its order chosen by BIC. This is consistent when the regressors are only pre-determined (they react to past shocks), where OLS and Cochrane-Orcutt are not. A variance estimator accounts for the estimated filter.
- Heteroskedasticity of unknown form (González-Coya and Perron, 2024). An adaptive Lasso of the log squared residuals on candidate covariates gives the weights, and a bias-corrected sandwich variance keeps inference valid when the variance model is wrong. If nothing is selected, FGLS equals OLS.
- Both together (Supplement S-4 of the 2026 paper).
It is the R counterpart of the Python package pyfgls, and agrees with it to machine precision on deterministic quantities. More code by the author: https://emiliogcs.com/code/.
Installation
# development version
# install.packages("pak")
pak::pak("emiliogcs/fgls")
# from CRAN, once released
install.packages("fgls")
Serial correlation with a non-exogenous regressor
library(fgls)
sim <- simulate_serial(500, seed = 1) # design of Table 1 of the 2026 paper; true slope 1
fit <- serial_fgls(y ~ x, data = sim)
summary(fit)
#>
#> Call:
#> serial_fgls(formula = y ~ x, data = sim)
#>
#> Method: FGLS (serial)
#> Covariance: robust
#> Observations: 500 (effective 499)
#> Inference: normal
#> AR order k*: 1 [BIC, kmax = 15]
#> AR coefficients: 0.7800
#> Non-exogeneity share: 0.011
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.11877 0.20552 5.444 5.22e-08 ***
#> x 0.98062 0.02517 38.967 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Notes:
#> [1] Covariance: PG26 eq. (29), robust to non-exogenous (pre-determined)
#> regressors.
#> [2] Collinear lagged columns dropped from the Durbin regression:
#> L1.(Intercept).
compare_fgls(OLS = lm(y ~ x, data = sim), FGLS = fit)
#> term statistic OLS FGLS
#> 1 (Intercept) estimate 1.12860678 1.11876951
#> 2 (Intercept) std.error 0.09034505 0.20551635
#> 3 (Intercept) ci.width 0.35414609 0.80560929
#> 4 x estimate 1.32962748 0.98062019
#> 5 x std.error 0.05108277 0.02516513
#> 6 x ci.width 0.20024076 0.09864549
Heteroskedasticity of unknown form
het <- simulate_hetero(200, skedastic = "log2", seed = 2)
fit_h <- lasso_fgls(y ~ x, data = het, seed = 1)
fit_h$skedastic$selected
#> [1] "log(x)" "cos(x)"
compare_fgls(OLS = lm(y ~ x, data = het), FGLS = fit_h)
#> term statistic OLS FGLS
#> 1 (Intercept) estimate 0.98861426 0.98253777
#> 2 (Intercept) std.error 0.18311445 0.08973843
#> 3 (Intercept) ci.width 0.71779546 0.35176818
#> 4 x estimate 1.02852565 1.03190100
#> 5 x std.error 0.09523622 0.06032162
#> 6 x ci.width 0.37331913 0.23645640
Both
both <- simulate_combined(200, ar = 0.5, skedastic = "x2", seed = 3)
fit_b <- fgls(y ~ x, data = both, seed = 1)
fit_b
#>
#> Call:
#> fgls(formula = y ~ x, data = both, seed = 1)
#>
#> F-CH (serial+hetero); AR order k* = 1 (BIC), rho = 0.4976; skedastic fit: lasso (selected: x, log(x)); covariance: robust
#>
#> Coefficients:
#> (Intercept) x
#> 1.5934 0.8101
See vignette("fgls") to get started, and the articles on serial
correlation,
heteroskedasticity,
the combined
estimator and the
validation
against the papers and pyfgls.
Citation
Perron P, González-Coya E (2026). “Feasible GLS for Time Series Regression.” Journal of Econometrics, 258, 106346. doi:10.1016/j.jeconom.2026.106346 https://doi.org/10.1016/j.jeconom.2026.106346.
González-Coya E, 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 https://doi.org/10.1515/jem-2023-0007.
González-Coya E (2026). fgls: Feasible GLS for Serial Correlation and Heteroskedasticity. R package version 0.1.0, https://github.com/emiliogcs/fgls.