Compute equality test between correlation coefficient estimates at two time points

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").

Value

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

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

## Simple example

res <- with(stockprice, tcor(x = SP500, y = FTSE100, t = DateID, h = 50, CI = TRUE))
test_equality(res)
#> The bandwidth stored in `tcor_obj` and used by `test_equality()` has not been automatically selected but was set by the user. Rerun `tcor()` without specifying `h` if you want otherwise.
#>           t1        r1         t2        r2   delta_r SE_delta_r   T_stat   df
#> 1 2000-04-03 0.3484362 2017-12-04 0.5800026 0.2315664  0.1798866 1.287291 8650
#>           p
#> 1 0.1980274

## Chi2 instead of Student's t-test

test_equality(res, test = "chi2")
#> The bandwidth stored in `tcor_obj` and used by `test_equality()` has not been automatically selected but was set by the user. Rerun `tcor()` without specifying `h` if you want otherwise.
#>           t1        r1         t2        r2   delta_r SE_delta_r chi2_stat df
#> 1 2000-04-03 0.3484362 2017-12-04 0.5800026 0.2315664  0.1798866  1.657118  1
#>           p
#> 1 0.1979929


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

test_equality(res, t1 = "2000-04-04", t2 = 1000)
#> The bandwidth stored in `tcor_obj` and used by `test_equality()` has not been automatically selected but was set by the user. Rerun `tcor()` without specifying `h` if you want otherwise.
#>           t1        r1         t2       r2     delta_r SE_delta_r     T_stat
#> 1 2000-04-04 0.3485947 2004-06-04 0.260934 -0.08766079  0.1766849 -0.4961421
#>     df         p
#> 1 8650 0.6198068
res[1000, "t"] ## t2 matches with date in `res`
#> [1] "2004-06-04"
stockprice[1000, "DateID"] ## t2 does not match with date `stockprice` due to missing values
#> # A tibble: 1 × 1
#>   DateID    
#>   <date>    
#> 1 2004-02-02


## 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)
#> The bandwidth stored in `tcor_obj` and used by `test_equality()` has not been automatically selected but was set by the user. Rerun `tcor()` without specifying `h` if you want otherwise.
#>           t1        r1         t2         r2    delta_r SE_delta_r    T_stat
#> 1 2000-04-04 0.3485947 2004-02-02 0.06689227 -0.2817025   0.180182 -1.563433
#>     df         p
#> 1 8650 0.1179874
res[1000, "t"] ## t2 matches with date in `res`
#> [1] "2004-06-04"
stockprice[1000, "DateID"] ## t2 does match with date `stockprice` despite missing values
#> # A tibble: 1 × 1
#>   DateID    
#>   <date>    
#> 1 2004-02-02