Trend Extraction Methods

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. All of them have defaults, so you can leave them unset.

window — number of observations in the smoothing window.
smoothing — amount of smoothing. The scale depends on the method; see Reading smoothing.
band — c(low, high), the cycle periods removed by a bandpass filter.
align — "center" (default) or "right", which uses only past and current observations. ma and wma also accept "left".
params — a named list for any remaining method-specific option.

# 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
)

Some defaults follow the frequency of the series. For monthly data the HP lambda defaults to 129600 and the ma, wma, and triangular windows to 12; for quarterly data, to 1600 and 4. The HP default scales 1600 by the fourth power of the frequency ratio (Ravn and Uhlig 2002), which gives 6.25 for annual data. This keeps the trend-cycle cutoff near ten years at every frequency. The band default covers cycles of 1.5 to 8 years: c(6, 32) for quarterly data and c(18, 96) for monthly.

Reading `smoothing`

The same number means different things to different methods.

hp: a value above 1 is the lambda itself. A value of 1 or less is a fraction of the frequency’s standard lambda, so smoothing = 0.5 on monthly data gives lambda = 64800.
loess: the span, the share of observations in each local fit.
spline: the spar penalty. Left unset, spline picks it by generalised cross-validation.
ewma: the weight alpha on the newest observation. Pass either window or smoothing to ewma, not both.
kernel: a multiplier on the automatically chosen bandwidth.
kalman: the ratio of measurement noise to process noise in a local-level model. Larger values give a smoother trend.

Method catalogue

Method	Description	Typical use	`window`	`smoothing`	`band`	`align`	One-sided
`hp`	Hodrick-Prescott filter	General-purpose business-cycle trend		✓			optional
`bn`	Beveridge-Nelson decomposition	Permanent component of an I(1) series
`ucm`	Unobserved components model	Model-based, stochastic trend
`hamilton`	Hamilton regression filter	Regression-based alternative to HP
`bk`	Baxter-King bandpass filter	Remove a band of cycle frequencies			✓
`cf`	Christiano-Fitzgerald bandpass filter	Band removal that keeps the endpoints			✓
`ma`	Simple moving average	Quick, intuitive smoothing	✓ vector			✓	optional
`spencer`	Spencer’s 15-term moving average	Classic actuarial graduation
`ewma`	Exponentially weighted moving average	Real-time, recent points weigh more	✓	✓			✓
`wma`	Weighted moving average	Smoothing with custom weights	✓			✓	optional
`triangular`	Triangular moving average	Smoother than a simple moving average	✓			✓	optional
`median`	Median filter	Smoothing robust to outliers and spikes	✓ vector
`gaussian`	Gaussian-weighted moving average	Smooth, bell-weighted average	✓			✓	optional
`henderson`	Henderson moving average	Trend filter used inside X-11	✓ vector
`stl`	Seasonal-trend decomposition via Loess	Trend of a strongly seasonal series	✓
`loess`	Local polynomial regression (loess)	Flexible non-parametric trend		✓
`spline`	Smoothing splines	Smooth curve, GCV penalty by default		✓
`poly`	Polynomial trend	Simple global trend shape
`kernel`	Kernel smoother	Non-parametric, bandwidth-controlled		✓
`kalman`	Kalman filter/smoother	Local-level trend of a noisy series		✓

Every method also accepts method-specific options through params. A few entries in the table need a note.

stl: window sets the seasonal window (s.window), not the trend window. Set the trend window with params = list(t.window = ...).
vector: pass several windows, such as window = c(13, 23), to get one trend per window.
triangular and gaussian accept align = "center" or "right" only.
One-sided methods use only past and current observations, which matters for real-time work. ewma is always one-sided. The methods marked optional are one-sided with align = "right", or, for hp, with params = list(hp_onesided = TRUE).

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 the alignment through align. 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. stl and loess are locally adaptive; spline and kernel trade off fit against smoothness through a penalty or a 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 designed to avoid the spurious cycles HP can introduce; bn and ucm are model-based decompositions into permanent and transitory parts. For ucm, the default is a basic structural model ("BSM") for frequencies 2 to 12 and a local-level model otherwise. Its variances are estimated by maximum likelihood, so smoothing does not control this method; explicit BSM requests support frequencies up to 12.

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) isolate the fluctuations whose period falls inside a chosen band. The trend they return is the series minus that band: the long-run movement plus any high-frequency noise. To get the band itself, use detrend_series(). Specify the band with band = c(low, high), in periods of the series (months for monthly data). bk leaves missing values at both ends of the series; cf does not.

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.