Simple bivariate "Gershunov-test"

g_test.R

library(zoo)

g_test <- function(x, y, w = 20, l = 1000) {

  cor_fun <- function(x) cor(x[,1], x[,2])
  
  ## benchmark
  d0 <- data.frame(x, y)
  c0 <- rollapply(d0, width = w, cor_fun, by.column = FALSE)

  ## l simulations
  di <- lapply(1:l, function(f) {
    data.frame(x, rnorm(length(x), mean = mean(y), sd = sd(y)))
  })
  ci <- lapply(sim, function(x) rollapply(x, width = w, cor_fun,
                                          by.column = FALSE))
  ## get sds and compare
  s0 <- sd(c0)
  si <- sapply(ci, sd)
  ecdf(si)(s0)
}