Glossary
R: Cross-quantilogram computation (using the 'quantilogram' package)
A measure introduced by Han, Linton, Oka, and Whang (2016) for detecting and quantifying directional predictability between two time series at specific quantiles. It extends the quantilogram to bivariate settings, enabling researchers to test whether large negative returns in ...
title: Cross-Quantilogram
slug: cross-quantilogram
Definition
A measure introduced by Han, Linton, Oka, and Whang (2016) for detecting and quantifying directional predictability between two time series at specific quantiles. It extends the quantilogram to bivariate settings, enabling researchers to test whether large negative returns in one market predict large negative returns in another.
Why It Matters
Standard correlation and regression capture average relationships, but risk management is often concerned with tail behavior — what happens during extreme events. The cross-quantilogram reveals whether distress in one variable predicts distress in another at specific quantile levels, such as the 5th or 1st percentile. This makes it invaluable for studying financial contagion, systemic risk, and downside spillovers that traditional methods may miss entirely.
Example
A researcher investigates whether extreme losses in the US stock market predict extreme losses in emerging markets. Using the cross-quantilogram at the 0.05 quantile, they find a significant value at lag 1, indicating that a bad day in the US increases the probability of a similarly bad day in emerging markets the following day. At the median (0.50 quantile), no such relationship exists.
```r
library(quantilogram)
cq <- cross_qt(data$US, data$EM, quantile = 0.05, lag = 5)
plot(cq)
```
Related Terms
Software Notes
R: Use the quantilogram package for estimation and inference, including bootstrap-based confidence intervals. Python: No dedicated package exists; implement using NumPy and rolling quantile comparisons, or use the replication code provided by the original authors.
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