Feasible GLS for serially correlated errors (Perron and González-Coya, 2026)

Shortcut for fgls() with hetero = "none": the errors are approximated by an AR(k) process whose coefficients come from the Durbin regression and whose order is chosen by BIC (eq. 14), the data are quasi-differenced and OLS is applied (eq. 15). The default variance is the exogeneity-robust estimator of eqs. (28)–(29), valid when the regressors are only pre-determined.

Usage

serial_fgls(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  serial = c("auto", "fixed", "ma1"),
  vcov = c("robust", "naive", "HC0", "HC1", "HC2", "HC3", "bootstrap"),
  ar_order = NULL,
  kmax = NULL,
  ic = c("bic", "aic"),
  lagged_dep_vars = NULL,
  exog = c("predetermined", "exogenous"),
  ...
)

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().
serial: "auto" (default), "fixed" or "ma1" (GMA estimator for MA(1) errors, PG26 Section 5; its only variance is vcov = "robust", the GMA covariance \(s^2 (X^{*\prime} X^*)^{-1}\)).
vcov: "robust" (default, eq. 29), "naive" (eq. 27, exogenous regressors only), "HC0"–"HC3" (eq. 29 with heteroskedasticity weights) or "bootstrap" (sieve bootstrap).
ar_order: Fixed AR order (implies serial = "fixed").
kmax: Largest AR order considered: NULL (default, \(\lfloor 12 (T/200)^{1/4} \rfloor\)), an integer, or "theory" (\(\lfloor (T/\ln T)^{1/3} \rfloor\)). It is capped so that the Durbin regression uses at most half of the sample as regressors.
ic: Lag-order criterion: "bic" (default) or "aic".
lagged_dep_vars: Names (or positions) of model-matrix columns that are lags of the dependent variable (not available with serial = "ma1").
exog: Assumption on the regressors: "predetermined" (default) or "exogenous". Estimates do not depend on it; it sets the default of first_stage_correction and the notes of the summary.
...: Further arguments passed to fgls(), e.g. wallis_regressor, use_t, time, 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

sim <- simulate_serial(500, seed = 42)
fit <- serial_fgls(y ~ x, data = sim)
fit
#> 
#> Call:
#> serial_fgls(formula = y ~ x, data = sim)
#> 
#> FGLS (serial); AR order k* = 1 (BIC), rho = 0.7669; covariance: robust
#> 
#> Coefficients:
#> (Intercept)            x  
#>      0.8491       0.9918  
#> 
fit$ar_order
#> [1] 1
fit$nonexogeneity_share
#> [1] 0.009554577

# Lagged dependent variable among the regressors (Wallis recovery)
df <- data.frame(y = sim$y[-1], ylag = sim$y[-500], x = sim$x[-1])
serial_fgls(y ~ ylag + x, data = df, lagged_dep_vars = "ylag")
#> 
#> Call:
#> serial_fgls(formula = y ~ ylag + x, data = df, lagged_dep_vars = "ylag")
#> 
#> FGLS (serial); AR order k* = 1 (BIC), rho = 0.7837; covariance: robust
#> 
#> Coefficients:
#> (Intercept)         ylag            x  
#>     0.83336      0.01755      0.99401  
#>