create.gain {deseats}

Create Gain Function from a Linear Time Series Filter

Description

This function takes a coefficient series of a linear time series filter as an input and then returns the corresponding gain function as an R function.

Usage

create.gain(filter.coefs = c(1), zero.at = ceiling(length(filter.coefs)/2))

Arguments

filter.coefs

a numeric vector with the filter coefficients ordered by coefficient index; see details for more info.

zero.at

a numeric vector of length one that indicates the position of the coefficient for the present observation in filter.coefs; by default, the position is in the middle or just below the midpoint.

Details

This is a functional. The function returns a function that represents the gain function for the input filter filter.coefs. The returned function only has the argument lambda, which is the frequency for which the value of the gain function should be obtained.

Let (y_t) be the input series and (c_j) the linear filter; then the element c_j is the weight assigned to y_{t-j}. The corresponding index j is important for the order of the argument filter.coefs.

Value

The function returns a "gain function" function that has the numeric argument lambda only that represents frequencies to calculate the values of the gain function for.

Author(s)

• Dominik Schulz (Research Assistant) (Department of Economics, Paderborn University),
  Author and Package Creator

Examples

# Moving average with smoothing over three values
a <- 1 / 3
gain_ma <- create.gain(rep(a, 3))
lambda <- seq(0, 0.5, 0.001)
GF <- gain_ma(lambda)
plot(lambda, GF, type = "l")



# First differences filter
b <- c(1, -1)
gain_diff <- create.gain(b)
lambda <- seq(0, 0.5, 0.001)
GF2 <- gain_diff(lambda)
plot(lambda, GF2, type = "l")


# For a fully data-driven local linear trend + 
# trigonometric polynomial seasonality
# (Note: we get various filters for different observation time points)

xt <- EXPENDITURES
est <- deseats(log(xt), set_options(order_poly = 3))
ws <- est@weights[, , "Combined"]
l <- (length(ws[, 1]) - 1) / 2

lambda <- seq(0, 0.5, 0.001)
mat <- matrix(0, ncol = length(lambda), nrow = l + 1)
colF <- colorRampPalette(c("deepskyblue4", "deepskyblue"))
cols <- colF(l)

for (j in 1:(l + 1)) {

  gainF <- create.gain(ws[j, ], zero.at = j)
  mat[j, ] <- gainF(lambda)

}

matplot(lambda, t(mat), type = paste0(rep("l", l + 1), collapse = ""),
        lty = rep(1, l + 1), col = cols)
title(
  main = paste0(
    "Gain functions for the applied data-driven locally weighted ",
    "regression\napproach at boundary points and the first interior ",
    "point"
  )
)

# Same example as before but not for the trend but for the detrending filters
# (Note: we get various filters for different observation time points)

ll <- l * 2 + 1
mat2 <- mat

for (j in 1:(l + 1)) {

  zero.vec <- rep(0, ll)
  zero.vec[[j]] <- 1
  gainF <- create.gain(zero.vec - ws[j, ], zero.at = j)
  mat2[j, ] <- gainF(lambda)

}

matplot(lambda, t(mat2), type = paste0(rep("l", l + 1), collapse = ""),
        lty = rep(1, l + 1), col = cols)
title(
  main = paste0(
    "Gain functions for the applied data-driven detrending filter\n",
    "at boundary points and the first interior ",
    "point"
  )
)