test_ref: Test difference between correlation coefficient estimates and a value of reference

Description

This function tests whether smoothed correlation values are equal (H0) or not to a reference value (default = 0). The test is not described in Choi & Shin, 2021, but it is based on the idea behind test_equality().

Usage

test_ref(
  tcor_obj,
  t = tcor_obj$t,
  r_ref = 0,
  test = c("student", "chi2"),
  p.adjust.methods = c("none", "bonferroni", "holm", "hochberg", "hommel", "BH", "BY",
    "fdr")
)

Value

a data.frame with the result of the test, including the effect size (delta_r = r[t] - r_ref).

Arguments

tcor_obj: the output of a call to tcor() with CI = TRUE.
t: a vector of time point(s) used by the test (by default, all time points are considered).
r_ref: a scalar indicating the reference value for the correlation coefficient to be used in the test (default = 0).
test: a character string indicating which test to use ("student", the default; or "chi2").
p.adjust.methods: a character string indicating the method used to adjust p-values for multiple testing (see p.adjust(); default = "none").

Details

Two different test statistics can be used, one is asymptotically Student-t distributed under H0 and one is chi-square distributed. In practice, it seems to give very similar results.

Examples

Run this code

## Comparison of all correlation values to reference of 0.5

res <- with(stockprice, tcor(x = SP500, y = FTSE100, t = DateID, h = 300, CI = TRUE))
ref <- 0.5
test_against_ref <- test_ref(res, r_ref = ref)
head(test_against_ref)


## Plot to illustrate the correspondance with confidence intervals

plot(res$r ~ res$t, type = "l", ylim = c(0, 1), col = NULL)
abline(v = test_against_ref$t[test_against_ref$p > 0.05], col = "lightgreen")
abline(v = test_against_ref$t[test_against_ref$p < 0.05], col = "red")
points(res$r ~ res$t, type = "l")
points(res$upr ~ res$t, type = "l", lty = 2)
points(res$lwr ~ res$t, type = "l", lty = 2)
abline(h = ref, col = "blue")


## Test correlation of 0 a specific time points (using index or dates)

test_ref(res, t = c(100, 150))
test_ref(res, t = c("2000-08-18", "2000-10-27"))