Trend Extraction Methods • trendseries

library(trendseries)
library(ekioplot)

series_palette <- unname(c(
  ekio_pal("blue")["700"],
  ekio_pal("blue")["400"],
  ekio_pal("teal")["600"]
))
highlight_gold <- unname(ekio_pal("gold")["light"])
highlight_orange <- unname(ekio_pal("orange")["400"])

This article catalogues the trend-extraction methods in trendseries: what each one does, when to reach for it, and which parameters it accepts. For worked examples of specific filters, see the companion Moving Averages and Econometric Filters articles. To split a series into trend, seasonal, and remainder components instead of extracting a single smooth trend, see Decomposing Series.

The two interfaces

Two functions share the same engine and the same parameters, and either one reaches every method.

augment_trends() — pipe-friendly. Takes a data.frame/tibble, adds trend_{method} columns, and supports grouped series via group_cols.
extract_trends() — takes a ts/xts/zoo object and returns ts objects (a single ts for one method, a named list for several).

# Data-frame interface: adds a trend_stl column
head(augment_trends(ibcbr, value_col = "index", methods = "stl"))

# Time-series interface: returns a ts object
hp_trend <- extract_trends(AirPassengers, methods = "hp")
class(hp_trend)

Pass several methods at once to compare them.

trends <- augment_trends(
  ibcbr,
  value_col = "index",
  methods = c("hp", "stl", "henderson")
)
head(trends)

The unified parameter system

Rather than exposing every method’s idiosyncratic arguments, trendseries routes a small set of generic parameters to whichever method-specific option they correspond to. Each one has a frequency-aware default, so you can leave them unset.

Parameter	Applies to	Meaning
`window`	moving-average methods (`ma`, `wma`, `triangular`, `ewma`, `median`, `gaussian`, `stl`)	Number of observations in the smoothing window.
`smoothing`	`hp`, `loess`, `spline`, `ewma`, `kernel`, `kalman`	Amount of smoothing (interpretation varies by method).
`band`	bandpass filters (`bk`, `cf`)	`c(low, high)` cycle periods to keep.
`align`	`ma`, `wma`, `triangular`, `gaussian`	`"center"` (default), `"right"` (causal), or `"left"`.
`params`	all	A named list for any remaining method-specific options.

# A wider HP smoothing and a 5-month moving average, in one call
augment_trends(
  ibcbr,
  value_col = "index",
  methods = c("hp", "ma"),
  smoothing = 1600,
  window = 5
)

Frequency-aware defaults adapt to the data: for monthly series the HP smoothing parameter defaults to lambda = 14400 and the moving-average window to 12; for quarterly series, lambda = 1600 and a window of 4.

Method catalogue

Method	Description	Typical use
`hp`	Hodrick-Prescott filter	General-purpose business-cycle trend
`hamilton`	Hamilton regression filter	HP alternative without spurious cycles
`bn`	Beveridge-Nelson decomposition	Permanent/transitory split
`ucm`	Unobserved components model	Model-based, stochastic trend
`bk`	Baxter-King bandpass filter	Isolating a cycle frequency band
`cf`	Christiano-Fitzgerald bandpass filter	Asymmetric bandpass, uses endpoints
`ma`	Simple moving average	Quick, intuitive smoothing
`wma`	Weighted moving average	Smoothing with custom weights
`ewma`	Exponentially weighted moving average	Recent-weighted, real-time smoothing
`triangular`	Triangular moving average	Smoother than a simple MA
`median`	Median filter	Robust to outliers/spikes
`gaussian`	Gaussian-weighted moving average	Smooth, bell-weighted average
`spencer`	Spencer’s 15-term moving average	Classic actuarial graduation
`henderson`	Henderson moving average	Trend term inside X-11 seasonal adj.
`stl`	Seasonal-trend decomposition via Loess	Trend from strongly seasonal data
`loess`	Local polynomial regression	Flexible non-parametric trend
`spline`	Smoothing splines	Smooth curve with automatic penalty
`poly`	Polynomial trends	Simple global trend shape
`kernel`	Kernel smoother	Non-parametric, bandwidth-controlled
`kalman`	Kalman filter/smoother	Adaptive trend for noisy series

Moving averages

Moving-average methods replace each point with a (possibly weighted) average of its neighbours, which makes them a good starting point for exploratory work. Control the smoothing through window (and align for ‘left’, ‘center’, or ‘right’). ma, median, and henderson also accept a vector of windows, returning one trend per window.

augment_trends(
  ibcbr,
  value_col = "index",
  methods = "henderson",
  window = c(13, 23)
)

See Moving Averages for the full treatment.

Smoothing methods

Smoothing methods fit a flexible curve to the data. Methods like stl and loess are locally adaptive; spline and kernel trade off fit against smoothness through a penalty/bandwidth; poly imposes a single global shape. The smoothing parameter tunes how aggressively they smooth.

loess_trend <- extract_trends(AirPassengers, methods = "loess", smoothing = 0.3)
plot(AirPassengers, col = "grey60", ylab = "Air passengers")
lines(loess_trend, col = highlight_orange, lwd = 2)

Econometric filters

These are the typical filters of applied macroeconomics. The Hodrick-Prescott filter (hp) is perhaps the most widely used; hamilton is a regression-based alternative that attempts to avoid HP’s well-known spurious-cycle artefacts; bn and ucm are model-based decompositions into permanent and transitory parts.

augment_trends(
  gdp_construction,
  value_col = "index",
  methods = c("hp", "hamilton")
) |>
  head()

The HP filter has a one-sided (real-time) variant for nowcasting, where future observations must not influence the current estimate.

extract_trends(
  AirPassengers,
  methods = "hp",
  params = list(hp_onesided = TRUE)
) |>
  head()

See Econometric Filters for details.

Bandpass filters

Bandpass filters (bk, cf) keep only the fluctuations whose periodicity falls inside a chosen band, removing both the long-run trend and high-frequency noise. Specify the band with band = c(low, high) in periods (quarters for quarterly data).

extract_trends(
  AirPassengers,
  methods = "cf",
  band = c(18, 96)
) |>
  head()

Decomposition vs. trend extraction

The methods above estimate a single smooth trend. When you instead want to split a series into trend + seasonal + remainder, use decompose_series(), which has methods of its own.

Method	Engine	Notes
`stl`	`stats::stl()`	Loess-based, robust option available.
`regression`	OLS	Polynomial trend + seasonal dummies.
`classic`	`stats::decompose()`	Classical moving-average; additive or multiplicative.
`bsm`	`stats::StructTS()`	State-space model; components for every point.
`seats`	X-13ARIMA-SEATS	Requires the optional `seasonal` package.

decompose_series(gdp_construction, value_col = "index", methods = "stl") |>
  head()

The dedicated Decomposing Series article covers these in depth.

References

Ravn, M. O., & Uhlig, H. (2002). On adjusting the Hodrick-Prescott filter for the frequency of observations. The Review of Economics and Statistics, 84(2), 371–376.