test_equality {timevarcorr}

Compute equality test between correlation coefficient estimates at two time points

Description

This function tests whether smoothed correlation values at two time points are equal (H0) or not. The test is described page 341 in Choi & Shin (2021).

Usage

test_equality(
  tcor_obj,
  t1 = 1,
  t2 = nrow(tcor_obj),
  test = c("student", "chi2")
)

Arguments

tcor_obj

the output of a call to tcor() with CI = TRUE.

t1

the first time point used by the test (by default, the first time point in the time series).

t2

the second time point used by the test (by default, the last time point in the time series).

test

a character string indicating which test to use ("student", the default; or "chi2").

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.

Value

a data.frame with the result of the test, including the effect size (delta_r = r[t2] - r[t1]).

See Also

test_ref(), tcor()

Examples

## Simple example

res <- with(stockprice, tcor(x = SP500, y = FTSE100, t = DateID, h = 50, CI = TRUE))
test_equality(res)

## Chi2 instead of Student's t-test

test_equality(res, test = "chi2")


## Time point can be dates or indices (mixing possible) but output as in input data

test_equality(res, t1 = "2000-04-04", t2 = 1000)
res[1000, "t"] ## t2 matches with date in `res`
stockprice[1000, "DateID"] ## t2 does not match with date `stockprice` due to missing values


## It could be useful to use `keep.missing = TRUE` for index to match original data despite NAs

res2 <- with(stockprice, tcor(x = SP500, y = FTSE100, t = DateID,
                              h = 50, CI = TRUE, keep.missing = TRUE))
test_equality(res2, t1 = "2000-04-04", t2 = 1000)
res[1000, "t"] ## t2 matches with date in `res`
stockprice[1000, "DateID"] ## t2 does match with date `stockprice` despite missing values