Robust Trend-Cycle Estimation using the Henderson Filter

Estimates the trend-cycle component using Henderson moving averages robust to outliers (additive outliers and level shifts).

Usage

henderson_robust_smoothing(
  x,
  endpoints = c("Musgrave", "QL", "CQ", "DAF"),
  length = NULL,
  ao = NULL,
  ao_tc = NULL,
  ls = NULL,
  icr = NULL,
  local_icr = FALSE,
  asymmetric_var = FALSE,
  degree = 3,
  ...
)

Arguments

x

An input time series (object of class "ts" or "mts").

endpoints

Character string specifying the method used for asymmetric filters. By default, "musgrave" is used.

length

An integer specifying the length of the symmetric filter. If NULL, the length is selected automatically using x11_trend_selection().

ao

Vector of dates for Additive Outliers (AO) whose effects are allocated to the irregular component.

ao_tc

Vector of dates for Additive Outliers (AO) whose effects are allocated to the trend-cycle component.

ls

Vector of dates for Level Shifts (LS) whose effects are allocated to the trend-cycle component.

icr

Numeric value specifying the Irregular-to-Trend (I/C) ratio used for asymmetric filters.

local_icr

Logical. If TRUE, the I/C ratio is estimated locally (as described in Quartier-la-Tente, 2024) instead of globally.

asymmetric_var

Logical. When local_icr = TRUE, if TRUE, the variance is estimated for each asymmetric filter. If FALSE (the default), the variance associated with symmetric estimates is used throughout.

degree

Integer. When local_icr = TRUE, degree of the polynomial used to estimate the local bias parameter.

...

Additional arguments passed to rjd3filters::lp_filter().

Value

An object of class c("tc_estimates", "robust_henderson"). See tc_estimates() for a full description of the returned object.

Details

When outliers are present in a time series, standard linear filters like the Henderson moving average can spread their impact across adjacent trend estimates. This function explicitly accounts for specified Additive Outliers (AO) and Level Shifts (LS) during the filtering process to prevent distortion of the trend-cycle estimates as described in Quartier-la-Tente (2025).

In a nutshell, Henderson smoothing is equivalent to a local polynomial regression of degree 3 (or equivalently 2) estimated with weighted least squares, using specific weights to obtain the Henderson coefficients. Adding regressors to this local regression to account for outliers allows removing their influence on the estimation of polynomial coefficients and thus on the trend-cycle estimates.

References

Quartier-la-Tente, A. (2025). Estimation de la tendance-cycle avec des méthodes robustes aux points atypiques. https://github.com/AQLT/robustMA.

Examples

if (FALSE) { # rjd3jars::check_java_version(silent = TRUE)
x <- cars_registrations
outliers <- x13_regarima_outliers(x)
tc <- henderson_robust_smoothing(x, ao = outliers$ao, ls = outliers$ls, local_icr = TRUE)

tc_henderson <- henderson_smoothing(x)
plot(tc, xlim = c(2019, 2022))
lines(tc_henderson$tc, col = "blue")
}