kzFilter: (Adaptive) Kolmogorov-Zurbenko (KZ) Filter

In openair: Tools for the Analysis of Air Pollution Data

(Adaptive) Kolmogorov-Zurbenko (KZ) Filter

Description

kzFilter() applies a Kolmogorov-Zurbenko filter to one or more pollutant columns in a data frame at multiple window sizes and returns the decomposed components. The KZ filter is a low-pass filter formed by iterating a simple moving average k times with window size m. kzaFilter() applies an adaptive Kolmogorov-Zurbenko filter to one or more pollutant columns in a data frame at multiple window sizes and returns the decomposed components. The KZA filter uses a standard KZ filter to detect structural breaks and shrinks the window near those breaks to preserve sharp features.

Usage

kzFilter(
  mydata,
  pollutant = "o3",
  m = c(3L, 13L, 107L, 721L, 8761L),
  k = 5L,
  data.thresh = 0.25,
  type = "default",
  components = TRUE,
  comp.names = c("sub_day", "diurnal", "synoptic", "intermediate", "seasonal", "trend"),
  to_narrow = FALSE,
  ...
)

kzaFilter(
  mydata,
  pollutant = "o3",
  m = c(3L, 13L, 107L, 721L, 8761L),
  k = 5L,
  sensitivity = 1,
  data.thresh = 0.5,
  type = "default",
  components = TRUE,
  comp.names = c("sub_day", "diurnal", "synoptic", "intermediate", "seasonal", "trend"),
  to_narrow = FALSE,
  ...
)

Arguments

mydata	A data frame containing a date field in Date or POSIXct format. The input time series must be regular, e.g., hourly or daily.
pollutant	The name of a pollutant, e.g., pollutant = "o3". More than one pollutant can be supplied as a vector, e.g., pollutant = c("o3", "nox").
m	Integer vector of window sizes (kzFilter()) or maximum window sizes (kzaFilter()). Defaults to c(3, 13, 107, 721, 8761) (suited to hourly data). All values must be >= 3. Values of m should be odd; even values will produce a symmetric window of m + 1 points rather than m.
k	Integer. The number of iterations applied at each window size (kzFilter()) or the number of iterations for the baseline KZ filter used to detect structural breaks (kzaFilter()).
data.thresh	Numeric (0–1). Minimum fraction of valid (non-NA) values required within a window for a filtered value to be returned; otherwise NA is returned. Applies to the actual window size, which is smaller near the series edges. Default is 0.25 (25%).
type	Used for splitting the data further. Passed to cutData().
components	Logical. If TRUE (default) and more than one m value is supplied, component columns are added by differencing adjacent filtered series.
comp.names	Character vector of names for the component columns. Must have length length(m) + 1. Defaults to c("sub_day", "diurnal", "synoptic", "intermediate", "seasonal", "trend") to match the default m values. If the length does not match, numbered names (comp_1, comp_2, ...) are used with a warning.
to_narrow	Logical. If TRUE, return the data in tidy (long) format with a component column and a value column instead of one column per component. Intermediate filter columns (⁠kz(a)_*⁠) are dropped. Default is FALSE. Ignored when components = FALSE or a single m value is supplied.
...	Passed to cutData() for use with type.
sensitivity	Numeric. Controls how aggressively the window shrinks at structural breaks (higher = more aggressive). Used in kzaFilter().

Value

When to_narrow = FALSE (default), a tibble with the original columns plus intermediate filter columns (⁠kz(a)_{m}⁠) and component columns. When to_narrow = TRUE, a tidy tibble with a component column (factor ordered fast to slow) and a value column.

Default window sizes

With the default window sizes of 3, 13, 107, 721 and 8761 (suited to hourly data), the function returns six intermediate filtered columns and six physical components derived by differencing:

• sub_day — Short intra-day variations (⁠pollutant - kz(a)_3⁠)

• diurnal — daily cycle (⁠kz(a)_3 - kz(a)_13⁠)

• synoptic — 1–10 day weather systems (⁠kz(a)_13 - kz(a)_107⁠)

• intermediate — weekly to monthly variability (⁠kz(a)_107 - kz(a)_721⁠)

• seasonal — monthly to annual variability (⁠kz(a)_721 - kz(a)_8761⁠)

• trend — multi-year trend (⁠kz(a)_8761⁠)

Edge effects

At the start and end of the series the filter window is silently truncated rather than padded, so no NAs are introduced. However, values within the affected boundary zone are averaged over fewer points than the interior and should be interpreted with caution.

The affected length at each end of the series for a single filter pass is floor(m / 2) observations. Because the filter is iterated k times (each pass consuming the output of the previous one), the total affected zone at each end is approximately k * floor(m / 2) observations. With the default m = c(3, 13, 107, 721, 8761) and k = 5, the affected zones are roughly 5 h, 30 h (~1 day), 265 h (~11 days), 1,800 h (~75 days), and 21,900 h (~2.5 years) at each end respectively. The trend component therefore requires at least 5–6 years of data for the interior estimates to be unaffected.

Author(s)

David Carslaw

Examples

## Not run: 
# Default: 5 window sizes, 6 descriptively named components returned
mydata <- kzFilter(mydata, pollutant = "nox")

# Tidy long format
mydata <- kzFilter(mydata, pollutant = "nox", to_narrow = TRUE)

# Single window size (no component decomposition)
mydata <- kzFilter(mydata, pollutant = "nox", m = 24, k = 5)

## End(Not run)

## Not run: 
# Default: 5 window sizes, 6 descriptively named components returned
mydata <- kzaFilter(mydata, pollutant = "nox")

# Tidy long format
mydata <- kzaFilter(mydata, pollutant = "nox", to_narrow = TRUE)

# Single window size (no component decomposition)
mydata <- kzaFilter(mydata, pollutant = "nox", m = 24, k = 5)

## End(Not run)

openair documentation built on May 20, 2026, 5:07 p.m.