The `quantilogram`

package provides estimation and
inference methods for the cross-quantilogram. The cross-quantilogram is
a measure of nonlinear dependence between two variables, based on either
unconditional or conditional quantile functions. It can be considered an
extension of the correlogram, which is a correlation function over
multiple lag periods that mainly focuses on linear dependency.

This package allows users to detect the presence of directional predictability from one time series to another and provides a statistical inference method based on the stationary bootstrap.

You can install the released version of quantilogram from CRAN with:

`install.packages("quantilogram")`

Here’s a basic example of how to use the quantilogram package:

```
library(quantilogram)
# Load example data
data("sys.risk")
# Select two variables
= sys.risk[, c("JPM", "Market")]
D
# Set parameters
= 1 # lag order
k = seq(0.05, 0.95, 0.05) # a list of quantiles
vec.q = 200 # Repetition of bootstrap
B.size
# Compute and plot cross-quantilogram
= heatmap.crossq(D, k, vec.q, B.size)
res
# Display the plot
print(res$plot)
```

For more detailed examples and function descriptions, please refer to the package documentation.

The methods implemented in this package are based on the following key publications:

Linton, O., and Whang, Y. J. (2007). The quantilogram: With an application to evaluating directional predictability. Journal of Econometrics, 141(1), 250-282. doi:10.1016/j.jeconom.2007.01.004

Han, H., Linton, O., Oka, T., and Whang, Y. J. (2016). The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series. Journal of Econometrics, 193(1), 251-270. doi:10.1016/j.jeconom.2016.03.001

This package is free and open source software, licensed under GPL (>= 3).