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Emilio González Coya

Benchmark estimators

Source: R/benchmarks.R
ols_robust.Rd

Estimators used as comparisons in the papers and in compare_fgls():

Usage

ols_robust(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  vcov = c("HAC", "NW", "HC0", "HC1", "HC2", "HC3", "nonrobust"),
  kernel = NULL,
  bandwidth = NULL,
  small_sample = FALSE,
  use_t = FALSE,
  time = NULL,
  allow_gaps = FALSE,
  model = TRUE
)

cochrane_orcutt(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  ar_order = 1L,
  iterate = FALSE,
  max_iter = 100L,
  tol = 1e-08,
  use_t = FALSE,
  time = NULL,
  allow_gaps = FALSE,
  model = TRUE
)

durbin_estimator(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  ar_order = NULL,
  kmax = NULL,
  use_t = FALSE,
  time = NULL,
  allow_gaps = FALSE,
  model = TRUE
)

infeasible_gls(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  rho = NULL,
  omega = NULL,
  use_t = FALSE,
  time = NULL,
  allow_gaps = FALSE,
  model = TRUE
)

hybrid_gls(
  formula,
  data,
  subset,
  na.action = stats::na.fail,
  alpha = 0.05,
  lags = 1L,
  seed = NULL,
  use_t = FALSE,
  time = NULL,
  allow_gaps = FALSE,
  model = TRUE
)

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().

vcov

Covariance estimator for ols_robust().

kernel, bandwidth

Optional overrides for the HAC estimator: kernel "qs" or "bartlett", bandwidth "andrews", "nw" or a positive number.

small_sample

Multiply HAC covariances by \(T/(T-q)\).

use_t

Use Student-t (n_eff - q degrees of freedom) instead of normal inference.

time

Time index for data frames: the name of a Date, POSIXct or numeric column of data, or a vector with one value per row. It is used to check that rows are sorted and have no gaps, and must have no missing values in the sample. Convert character dates first, e.g. with as.Date() or zoo::as.yearmon().

allow_gaps

Accept a time index with gaps, or a subset that skips rows (lags are then positional), with a warning.

model

Keep the model frame in the result.

ar_order

AR order (cochrane_orcutt(), durbin_estimator()).

iterate

Iterate Cochrane-Orcutt to convergence.

max_iter, tol

Iteration limit and convergence tolerance.

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.

rho, omega

Known AR coefficients or known error covariance matrix.

alpha

Level of the Breusch-Godfrey test (hybrid_gls()), strictly between 0 and 1.

lags

Number of lags of the Breusch-Godfrey test, a positive integer.

seed

Optional seed for the random AR(1) coefficient that hybrid_gls() draws when the Breusch-Godfrey test rejects. The session's random number generator state is restored afterwards.

Value

An object of class "fgls" (see fgls()). The non-exogeneity share of PG26 eq. (29) is not computed for these estimators and is NA.

Details

  • ols_robust(): ordinary least squares with heteroskedasticity and autocorrelation consistent standard errors (vcov = "HAC": Andrews' 1991 quadratic-spectral kernel with automatic bandwidth, the benchmark of PG26; "NW": Newey-West Bartlett kernel with \(\lfloor 4 (T/100)^{2/9} \rfloor\) lags) or White-type standard errors ("HC0"–"HC3").

  • cochrane_orcutt(): two-step (or iterated) Cochrane-Orcutt FGLS. The two-step version estimates the AR coefficients from OLS residuals and is not valid with non-exogenous regressors (PG26 Section 3); use serial_fgls() instead.

  • durbin_estimator(): the Durbin regression (PG26 eq. 14) of \(y_t\) on \(y_{t-j}\), \(x_t\) and \(x_{t-j}\), \(j = 1, \dots, k\), with the AR order \(k\) chosen by BIC unless given. The coefficients on the stochastic regressors are those on \(x_t\). Lags of the constant, of trends and of periodic dummies are collinear with the regressors and dropped, so the Durbin coefficients \(c\) on these regressors estimate \((I - \sum_j \rho_j P_j)\beta\), where the dropped lags are \(x_{t-j} = x_t P_j\) (plus kept lags). They are converted back to \(\hat\beta = (I - \sum_j \hat\rho_j P_j)^{-1} c\), e.g. \(c / (1 - \sum_j \hat\rho_j)\) for the intercept, with a delta-method covariance, and are NA (with a note) when that is not possible. Residuals, fitted values and predictions use these coefficients; innovations are the residuals of the Durbin regression. (The Python package 'pyfgls' reports the untransformed \(c\).)

  • infeasible_gls(): GLS with known AR coefficients (rho) or a known error covariance matrix (omega, up to scale); a simulation benchmark.

  • hybrid_gls(): the hybrid OLS/GLS estimator of PG26 Supplement S-1 (exogenous regressors only): OLS when the Breusch-Godfrey test does not reject, otherwise quasi-differencing with a random AR(1) coefficient of the sign of the first-order residual autocorrelation.

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(300, seed = 1)
ols_robust(y ~ x, data = sim)
#> 
#> Call:
#> ols_robust(formula = y ~ x, data = sim)
#> 
#> OLS; covariance: HAC (QS, bw = 2.03)
#> 
#> Coefficients:
#> (Intercept)            x  
#>       1.163        1.341  
#> 
cochrane_orcutt(y ~ x, data = sim)
#> 
#> Call:
#> cochrane_orcutt(formula = y ~ x, data = sim)
#> 
#> Cochrane-Orcutt (two-step); AR order k* = 1 (cochrane-orcutt), rho = 0.6133; covariance: nonrobust
#> 
#> Coefficients:
#> (Intercept)            x  
#>       1.178        1.013  
#> 
durbin_estimator(y ~ x, data = sim)
#> 
#> Call:
#> durbin_estimator(formula = y ~ x, data = sim)
#> 
#> Durbin; AR order k* = 1 (durbin), rho = 0.7654; covariance: nonrobust
#> 
#> Coefficients:
#> (Intercept)            x  
#>      1.1858       0.9938  
#> 
infeasible_gls(y ~ x, data = sim, rho = 0.8)
#> 
#> Call:
#> infeasible_gls(formula = y ~ x, data = sim, rho = 0.8)
#> 
#> GLS (infeasible); AR order k* = 1 (known), rho =   0.8; covariance: nonrobust
#> 
#> Coefficients:
#> (Intercept)            x  
#>      1.1915       0.9827  
#>