stl2: Seasonal Decomposition of Time Series by Loess

In hafen/stl2: Implementation of Seasonal-Trend Decomposition using Loess (STL) in R

Description

Decompose a time series into seasonal, trend and irregular components using loess, acronym STL. A new implementation of STL. Allows for NA values, local quadratic smoothing, post-trend smoothing, and endpoint blending. The usage is very similar to that of R's built-in stl().

Usage

stl2(x, t = NULL, n.p, s.window, s.degree = 1, 
   t.window = NULL, t.degree = 1, 
   fc.window = NULL, fc.degree = NULL, fc.name = NULL, 
   l.window = NULL, l.degree = t.degree, 
   s.jump=ceiling(s.window/10), t.jump=ceiling(t.window/10), 
   l.jump=ceiling(l.window/10), fc.jump = NULL, 
   critfreq = 0.05, s.blend = 0, t.blend = 0, 
   l.blend = t.blend, fc.blend=NULL, 
   inner = 2, outer = 1, 
   sub.labels = NULL, sub.start=1, details = FALSE,
   ...)

Arguments

x	vector of time series values, in order of time. If x is a time series object, then t and n.p do not need to be specified, although they still can be.
t	times at which the time series values were observed. Not required.
n.p	periodicity of the seasonal component. In R's stl function, this is the frequency of the time series.
s.window	either the character string "periodic" or the span (in lags) of the loess window for seasonal extraction, which should be odd. This has no default.
s.degree	degree of locally-fitted polynomial in seasonal extraction. Should be 0, 1, or 2.
t.window	the span (in lags) of the loess window for trend extraction, which should be odd. If NULL, the default, nextodd(ceiling((1.5*period) / (1-(1.5/s.window)))), is taken.
t.degree	degree of locally-fitted polynomial in trend extraction. Should be 0, 1, or 2.
l.window	the span (in lags) of the loess window of the low-pass filter used for each subseries. Defaults to the smallest odd integer greater than or equal to n.p which is recommended since it prevents competition between the trend and seasonal components. If not an odd integer its given value is increased to the next odd one.
l.degree	degree of locally-fitted polynomial for the subseries low-pass filter. Should be 0, 1, or 2.
critfreq	the critical frequency to use for automatic calculation of smoothing windows for the trend and high-pass filter.
fc.window	vector of lengths of windows for loess smoothings for other trend frequency components after the original STL decomposition has been obtained. The smoothing is applied to the data with the STL seasonal component removed. A frequency component is computed by a loess fit with the window length equal to the first element of fc.window, the component is removed, another component is computed with the window length equal to the second element of fc.window, and so forth. In most cases, the values of the argument should be decreasing, that is, the frequency bands of the fitted components should increase. The robustness weights from original STL are used as weights in the loess fitting if specified.
fc.degree	vector of degrees of locally-fitted polynomial in the loess smoothings for the frequency components specified in fc.window. Values of 0, 1 and 2 are allowed. If the length of fc.degree is less than that of fc.window, the former is expanded to the length of the latter using rep; thus, giving the value 1 specifies a degree of 1 for all components.
fc.name	vector of names of the post-trend smoothing operations specified by fc.window and fc.degree (optional).
inner	integer; the number of ‘inner’ (backfitting) iterations; usually very few (2) iterations suffice.
outer	integer; the number of ‘outer’ robustness iterations. Default is 0, but Recommended if outliers are present.
sub.labels	optional vector of length n.p that contains the labels of the subseries in their natural order (such as month name, day of week, etc.), used for strip labels when plotting. All entries must be unique.
sub.start	which element of sub.labels does the series begin with. See details.
details	if TRUE, returns a list of the results of all the intermediate iterations.
s.jump, t.jump, l.jump, fc.jump	integers at least one to increase speed of the respective smoother. Linear interpolation happens between every *.jumpth value.
s.blend, t.blend, l.blend, fc.blend	vectors of proportion of blending to degree 0 polynomials at the endpoints of the series.
...

Details

The seasonal component is found by loess smoothing the seasonal sub-series (the series of all January values, ...); if s.window = "periodic" smoothing is effectively replaced by taking the mean. The seasonal values are removed, and the remainder smoothed to find the trend. The overall level is removed from the seasonal component and added to the trend component. This process is iterated a few times. The remainder component is the residuals from the seasonal plus trend fit.

Cycle-subseries labels are useful for plotting and can be specified through the sub.labels argument. Here is an example for how the sub.labels and sub.start parameters might be set for one situation. Suppose we have a daily series with n.p=7 (fitting a day-of-week component). Here, sub.labels could be set to c("Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"). Now, if the series starts with a Wednesday value, then one would specify sub.labels=4, since Wednesday is the fourth element of sub.labels. This ensures that the labels in the plots to start the plotting with Sunday cycle-subseries instead of Wednesday.

Value

returns an object of class "stl2", containing

data	data frame containing all of the components: raw, seasonal, trend, remainder, weights.
pars	list of parameters used in the procedure.
fc.number	number of post-trend frequency components fitted.
fc	data frame of the post-trend frequency components.
time	vector of time values corresponding to the raw values, if specified.
n	the number of observations.
sub.labels	the cycle-subseries labels.

Note

This is a complete re-implementation of the STL algorithm, with the loess part in C and the rest in R. Moving a lot of the code to R makes it easier to experiment with the method at a very minimal speed cost. Recoding in C instead of using R's built-in loess results in better performance, especially for larger series.

Author(s)

Ryan Hafen

References

R. B. Cleveland, W. S. Cleveland, J. E. McRae, and I. Terpenning (1990) STL: A Seasonal-Trend Decomposition Procedure Based on Loess. Journal of Official Statistics, 6, 3–73.

See Also

plot.stl2 for plotting the components.

getraw, seasonal, trend, remainder for accessing the components.

Examples

co2.stl <- stl2(co2, t=as.vector(time(co2)), n.p=12, 
   l.window=13, t.window=19, s.window=35, s.degree=1, 
   sub.labels=substr(month.name, 1, 3))

plot(co2.stl, ylab="CO2 Concentration (ppm)", xlab="Time (years)")
plot.seasonal(co2.stl)
plot.trend(co2.stl)
plot.cycle(co2.stl)
plot.rembycycle(co2.stl)

# post-trend smoothing

co2.stl_pt <- stl2(co2, t=as.vector(time(co2)), n.p=12, 
   l.window=13, t.window=19, s.window=35, s.degree=1, 
   sub.labels=substr(month.name, 1, 3), 
   fc.degree=c(1, 2), fc.window=c(201, 35), 
   fc.name=c("long-term", "so. osc."))

plot(co2.stl_pt, scales=list(y=list(relation="free")), 
   ylab="CO2 Concentration (ppm)", xlab="Time (years)", 
   aspect=0.25, type=c("l", "g"))

# with NAs

y <- co2
y[201:224] <- NA

y.stl <- stl2(y, l.window=13, t.window=19, s.window=35, 
   s.degree=1, sub.labels=substr(month.name, 1, 3))

plot(y.stl, ylab="CO2 Concentration (ppm)", xlab="Time (years)")
plot.seasonal(y.stl)
plot.trend(y.stl)
plot.cycle(y.stl)
plot.rembycycle(y.stl)

# if you don't want to use a time series object:
y.stl <- stl2(y, t=as.vector(time(y)), n.p=12, 
   l.window=13, t.window=19, s.window=35, s.degree=1, 
   sub.labels=substr(month.name, 1, 3))


# with an outlier
y2 <- co2
y2[200] <- 300

y2.stl <- stl2(y2, t=as.vector(time(y2)), n.p=12, 
   l.window=13, t.window=19, s.window=35, s.degree=1, 
   sub.labels=substr(month.name, 1, 3), outer=10)

plot(y2.stl, ylab="CO2 Concentration (ppm)", xlab="Time (years)")
plot.seasonal(y2.stl)
plot.trend(y2.stl)
plot.cycle(y2.stl)
plot.rembycycle(y2.stl)

# compare to R's stl

x1 <- stl2(co2, t=as.vector(time(co2)), n.p=12, 
   l.window=13, t.window=19, s.window=11, s.degree=1, 
   sub.labels=substr(month.name, 1, 3))

x2 <- stl(co2, l.window=13, t.window=19, s.window=11, s.degree=1)

# will be different due to interpolation differences
plot(seasonal(x1) - seasonal(x2))

# but not if all jump parameters are 1
x1 <- stl2(co2, t=as.vector(time(co2)), n.p=12, 
   l.window=13, t.window=19, s.window=11, s.degree=1, 
   sub.labels=substr(month.name, 1, 3), 
   s.jump=1, t.jump=1, l.jump=1)

x2 <- stl(co2, l.window=13, t.window=19, s.window=11, s.degree=1,
   s.jump=1, t.jump=1, l.jump=1)

plot(seasonal(x1) - seasonal(x2))

hafen/stl2 documentation built on May 17, 2019, 2:23 p.m.