Linear Filtering on a Time Series

Applies linear filtering to a univariate time series or to each series separately of a multivariate time series using either a moving average (symmetric or asymmetric) or a combination of symmetric moving average at the center and asymmetric moving averages at the bounds.

Usage

filter(x, coefs, remove_missing = TRUE)

Arguments

x

a univariate or multivariate time series.

coefs

a matrix or a list that contains all the coefficients of the asymmetric and symmetric filters. (from the symmetric filter to the shortest). See details.

remove_missing

if TRUE (default) leading and trailing NA are removed before filtering.

Value

An object of the same class as x (ts, mts, vector or matrix) with the filtered time series.

Details

The functions filter extends filter allowing to apply every kind of moving averages (symmetric and asymmetric filters) or to apply a set of multiple moving averages to deal with the boundaries.

Let \(x_t\) be the input time series to filter.

• If coef is an object moving_average(), of length \(q\), the result \(y\) is equal at time \(t\) to: $$y[t] = x[t-lags] * coef[1] + x[t-lags+1] * coef[1] + ... + x[t-lags+q] * coef[q]$$. It extends the function filter that would add NA at the end of the time series.

• If coef is a matrix, list or finite_filters() object, at the center, the symmetric moving average is used (first column/element of coefs). At the boundaries, the last moving average of coefs is used to compute the filtered time series \(y[n]\) (no future point known), the second to last to compute the filtered time series \(y[n-1]\) (one future point known)...

Examples

x <- retailsa$DrinkingPlaces

lags <- 6
leads <- 2
fst_coef <- fst_filter(lags = lags, leads = leads, smoothness.weight = 0.3, timeliness.weight = 0.3)
lpp_coef <- lp_filter(horizon = lags, kernel = "Henderson", endpoints = "LC")

fst_ma <- filter(x, fst_coef)
lpp_ma <- filter(x, lpp_coef[,"q=2"])

graphics::plot(stats::ts.union(x, fst_ma, lpp_ma),
               plot.type = "single",
               col = c("black","red","blue"))


trend <- filter(x, lpp_coef)
# This is equivalent to:
trend <- localpolynomials(x, horizon = 6)