Skip to contents

publishTC

Why not publish the trend-cycle?

The goal of publishTC is to facilitate the computation, evaluation, and visualization of trend-cycle components from time series using modern state-of-the-art methodology:

  • Using the Cascade Linear Filter (CLF) and surrogate cut-and-normalise asymmetric filters, as done by Statistics Canada (Dagum and Luati 2008);
  • Using the classical Henderson symmetric filter and surrogate Musgrave asymmetric filters, as done by the Australian Bureau of Statistics (Trewin 2003);
  • Using a local parametrization of Musgrave asymmetric filters (Quartier-la-Tente 2024);
  • Extending Henderson filters to take into account additive outliers (AO) and level shifts (LS) (Quartier-la-Tente 2025).

Installation

To install publishTC:

install.packages('publishTC', repos = c('https://aqlt.r-universe.dev', 'https://cloud.r-project.org'))

Quick Start

1. Trend-Cycle Estimation

Estimate the trend-cycle component using the standard Henderson filter:

# Example dataset: French Industrial Production Index
x <- french_ipi[, "manufacturing"]

# Compute Henderson trend-cycle estimates
tc_hend <- henderson_smoothing(x, length = 13)

# Summary diagnostics (I/C ratio, MCD, filter length)
summary(tc_hend)
#> $`I/C ratio`
#> [1] 3.318081
#> 
#> $`I/C ratios`
#>  [1] 3.3180811 1.6933861 1.0927936 0.8358296 0.6684998 0.5812624 0.5760156
#>  [8] 0.5072746 0.4796632 0.4476804 0.4014496 0.4138149
#> 
#> $MCD
#> [1] 4
#> 
#> $Length
#> [1] 13

2. Multi-Method Comparison

Compare different trend-cycle estimation approaches on the same series:

# Estimate trend using multiple methods
all_tc <- smoothing(x)

# Plot comparison
plot(all_tc$henderson, xlim = c(2021, 2024.5))
lines(all_tc$henderson_localic, col_tc = "blue")

Comparison of trend-cycle estimation methods

3. Outlier-Robust & Segmented Smoothing

Account for Additive Outliers (AO) and Level Shifts (LS) during estimation:

# Identify outliers using RegARIMA wrapper
outliers <- x13_regarima_outliers(x)

# Compute robust Henderson trend-cycle estimates
tc_robust <- henderson_robust_smoothing(
  x, 
  ao = outliers$ao, 
  ls = outliers$ls, 
  local_icr = TRUE
)

# Segmented smoothing around a structural break
tc_seg <- segmented_smoothing(
  x, 
  breaks = list(c(2020, 3)), 
  break_method = "two-sides"
)
plot(tc_robust, xlim = c(2019, 2021))
lines(tc_seg, col_tc = "#009E73")
lines(tc_hend, col_tc = "#0072B2")
legend(
  "bottomleft",
  legend = c(
    "Seasonally adjusted (SA)", "Robust Henderson", 
    "Segmented", "Standard Henderson"
    ),
  col = c("black", "orange", "#009E73", "#0072B2"),
  lty = 1
)

4. Turning Point & Ripple Diagnostics

Identify economic turning points and short-term unwanted ripples:

# Find turning points (upturns and downturns)
tp <- turning_points(tc_hend)
tp
#> $upturn
#>  [1] 1990.667 1991.333 1993.750 1995.833 1998.917 2001.833 2002.833 2003.417
#>  [9] 2004.417 2005.333 2006.583 2007.667 2009.167 2012.833 2013.583 2014.667
#> [17] 2016.333 2018.083 2019.500 2020.250 2021.167 2022.917
#> 
#> $downturn
#>  [1] 1990.917 1991.833 1995.000 1998.417 2001.000 2002.167 2004.167 2004.833
#>  [9] 2006.333 2007.333 2008.000 2011.083 2013.167 2013.917 2015.833 2017.750
#> [17] 2019.083 2019.750 2020.667 2022.583 2023.500
# Count unwanted ripples (cycles under 11 months)
ripples <- unwanted_ripples(tc_hend)
ripples
#> [1] 30

Main Functions Overview

Category Main Functions
Estimation henderson_smoothing(), clf_smoothing(), henderson_robust_smoothing(), segmented_smoothing(), smoothing()
Diagnostics icr(), icrs(), mcd(), smoothness(), bandwidth(), turning_points(), unwanted_ripples(), implicit_forecasts(), underlying_forecasts()
Visualization (base R) plot(), lines(), lollypop(), implicit_forecasts_plot(), confint_plot(), growthplot(), implicit_forecasts_plot(), underlying_forecasts_plot()
Visualization (ggplot2) autoplot(), gglollypop(), ggconfint_plot(), ggsmoothing_plot(), gggrowthplot(), ggimplicit_forecasts_plot(), ggunderlying_forecasts_plot()
Utilities write.ts(), read.ts(), x13_regarima_outliers()

References

  • Dagum, E. B., & Luati, A. (2008). A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation. Econometric Reviews, 28(1-3), 40‑59. https://doi.org/10.1080/07474930802387837
  • Henderson, R. (1916). Note on graduation by adjusted average. Transactions of the Actuarial Society of America, 17, 43‑48.
  • Musgrave, J. (1964). A set of end weights to end all end weights. US Census Bureau [custodian].
  • Quartier-la-Tente, A. (2024). Improving Real-Time Trend Estimates Using Local Parametrization of Polynomial Regression Filters. Journal of Official Statistics, 40(4), 685-715. https://doi.org/10.1177/0282423X241283207
  • Quartier-la-Tente, A. (2025). Estimation de la tendance-cycle avec des méthodes robustes aux points atypiques. https://github.com/AQLT/robustMA
  • Trewin, D. (2003). A guide to interpreting time series - Monitoring trends. Australian Bureau of Statistics Information Paper. https://www.abs.gov.au/AUSSTATS/abs@.nsf/Lookup/1349.0Main+Features12003?OpenDocument