Recursive filter with time-varying coefficient

This is simply an AR(1) recursive filter with a time-varying recession rate.

filter_tv(x, a, init = 0)

Arguments

x: numeric vector or time series.
a: numeric vector the same length as x, giving the filter coefficient at each time step.
init: value for x[0].

Value

a numeric vector or time series, like x.

Note

If there are internal missing values, these are skipped over in the calculation, maintaining the "state": the value of y[i-1] after any missing values is the value from just before them. This behaviour is different from filter, which drops the state back to 0.

Author

Felix Andrews felix@nfrac.org

Examples


## The non-compiled function is this simple, if there are no NAs:
ftv2 <- function(x, a, init = 0) {
  y <- x
  y[1] <- x[1] + a[1] * init
  for (i in 2:length(x)) {
    y[i] <- x[i] + a[i] * y[i - 1]
  }
  return(y)
}
## make a sine wave filter
a <- sin(pi * seq(0, 3 * pi, length = 100)) * 0.2 + 0.9
plot.ts(a, ylim = c(0, 1.2))

## response to a unit impluse
x <- c(1, rep(0, 99))
y <- filter_tv(x, a)
plot.ts(y, log = "y")

stopifnot(isTRUE(all.equal(y, ftv2(x, a))))
## treatment of missing values
x[15:20] <- NA
plot.ts(filter_tv(x, a), log = "y")