Time Varying Correlation.
timevarcorr
This R package aims at measuring how the correlation between 2 time-series changes over time, following the method described in Choi & Shin (2021):
Choi, JE., Shin, D.W. Nonparametric estimation of time varying correlation coefficient. J. Korean Stat. Soc. 50, 333–353 (2021). doi:10.1007/s42952-020-00073-6
The chief idea is to perform a non-parametric kernel smoothing (using a common bandwidth) of all underlying components required for the computation of a correlation coefficient (i.e., $x$, $y$, $x^2$, $y^2$, $x*y$).
The automatic selection procedure for the bandwidth parameter proposed in the paper is implemented in this package. The same goes for the computation of confidence intervals.
We also implemented the possibility to use Epanechnikov, Gaussian, or box kernels, as well as to estimate either the Pearson or the Spearman correlation coefficient.
Installation
You can install the CRAN version of timevarcorr with:
install.packages("timevarcorr")
You can install the development version of timevarcorr from GitHub with:
# install.packages("remotes") ## uncomment and run if you don't have this package installed
remotes::install_github("courtiol/timevarcorr")
That should suffice!
Note that this package relies so far on only one direct dependency – lpridge – which itself depends on nothing but a plain R install.
Nonetheless, in some of the examples below, we also rely on dplyr and ggplot2, so you would need to install these packages as well to reproduce the content of this README:
install.packages("dplyr")
install.packages("ggplot2")
Examples
The main function of this package is called tcor and its documentation is available here:
help(tcor, package = timevarcorr)
Here is a very simple example using base-R syntax:
library(timevarcorr)
#> timevarcorr loaded; type ?tcor for help on this package.
d <- stockprice[1:500, ]
example1 <- with(d, tcor(x = SP500, y = FTSE100, t = DateID, kernel = "normal"))
#>
#> You may use several CPU cores for faster computation by calling `options('mc.cores' = XX)` with `XX` corresponding to the number of CPU cores to be used.
#> h selected using LOO-CV = 60.9
#> Bandwidth automatic selection completed in 9.1 seconds
plot(example1, type = "l")
Here is the same example using tidyverse syntax (with confidence interval):
library(dplyr)
library(ggplot2)
d |>
reframe(tcor(x = SP500, y = FTSE100, t = DateID,
kernel = "normal", CI = TRUE)) |>
ggplot() +
aes(x = t, y = r, ymin = lwr, ymax = upr) +
geom_ribbon(fill = "grey") +
geom_line() +
labs(title = "SP500 vs FTSE100", x = "Time", y = "Correlation") +
theme_classic()
And now, the same example showing gaps of observations in the time series:
d |>
reframe(tcor(x = SP500, y = FTSE100, t = DateID,
kernel = "normal", CI = TRUE, keep.missing = TRUE)) |>
ggplot() +
aes(x = t, y = r, ymin = lwr, ymax = upr) +
geom_ribbon(fill = "grey") +
geom_line() +
labs(title = "SP500 vs FTSE100", x = "Time", y = "Correlation") +
theme_classic()
#>
#> You may use several CPU cores for faster computation by calling `options('mc.cores' = XX)` with `XX` corresponding to the number of CPU cores to be used.
#> h selected using LOO-CV = 60.9
#> Bandwidth automatic selection completed in 8.7 seconds
You can do more. For example, you can use other kernels, fix the bandwidth manually, or use the Spearman’s rather than the Pearson’s correlation coefficient:
example2 <- with(d, tcor(x = SP500, y = FTSE100, t = DateID,
cor.method = "spearman", kernel = "box", h = 10))
plot(example2, type = "l")
You can also test the difference in correlation coefficients between two time points:
example3 <- with(d, tcor(x = SP500, y = FTSE100, t = DateID, kernel = "normal", CI = TRUE))
#>
#> You may use several CPU cores for faster computation by calling `options('mc.cores' = XX)` with `XX` corresponding to the number of CPU cores to be used.
#> h selected using LOO-CV = 60.9
#> Bandwidth automatic selection completed in 8.9 seconds
test_equality(example3, t1 = "2000-05-02", t2 = "2001-05-02")
#> t1 r1 t2 r2 delta_r SE_delta_r T_stat df
#> 1 2000-05-02 0.4354492 2001-05-02 0.5722 0.1367509 0.1224746 1.116565 910
#> p
#> 1 0.264475
Or you can test if specific time points (or all) differ from a reference value:
test_ref(example3, t = c("2000-05-02", "2001-05-02"), r_ref = 0.5)
#> t r r_ref delta_r SE_delta_r T_stat df p
#> 1 2000-05-02 0.4354492 0.5 -0.06455083 0.10082705 -0.6402134 910 0.5221950
#> 2 2001-05-02 0.5722000 0.5 0.07220003 0.06952644 1.0384542 910 0.2993345
#> p_adjustment
#> 1 none
#> 2 none
Devel corner
This README file has been compiled using devtools::build_readme(), with the following setup:
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