Cross-Quantilogram
The cross-quantilogram extends the cross-correlogram concept to quantile pairs of two time series, measuring dependence at different quantile levels. Introduced by Linton and Whang (2012), it captures how shocks at specific quantile levels in one series relate to movements in another, enabling asymmetric dependence analysis. This approach is particularly valuable when downside and upside risk correlations differ materially.
Key highlights
- Captures asymmetric and tail-dependent relationships invisible to standard correlation
- Flexible across quantile levels, allowing targeted analysis of extreme events
- Nonparametric approach requires fewer distributional assumptions
- Computes at different lags, revealing dynamic causality structures
Intuition
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How it works
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When to use it
Use cross-quantilogram when you suspect asymmetric dependence between series—for instance, when downside risk spillovers exceed upside risk, or when different market segments react differently to the same shock. It is particularly useful in financial econometrics for examining tail co-movements, credit-equity spillovers, and commodity-equity linkages. Assume stationarity of underlying series or apply appropriate transformations first.
Strengths & limitations
- Captures asymmetric and tail-dependent relationships invisible to standard correlation
- Flexible across quantile levels, allowing targeted analysis of extreme events
- Nonparametric approach requires fewer distributional assumptions
- Computes at different lags, revealing dynamic causality structures
- Computationally intensive for large datasets or many quantile pairs
- Requires larger sample sizes to estimate extreme quantiles reliably
- Interpretation becomes complex with many quantile combinations
- Sensitive to outliers and data quality in tail regions
Common pitfalls
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Applications
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Frequently asked
How does cross-quantilogram differ from standard cross-correlation?
Standard cross-correlation measures average linear dependence. Cross-quantilogram measures dependence conditional on specific quantile levels of each series, capturing asymmetries invisible to conventional methods. For example, you may find a stock and commodity are uncorrelated on average but strongly negatively correlated in the bottom 10% of returns.
What sample size is needed to estimate extreme quantiles reliably?
Estimating the 1st or 99th percentile requires at least 100–200 observations per quantile pair. For daily data, that is typically 6–12 months. For extreme tail quantiles (0.5%, 99.5%), consider 1000+ observations and use robust inference methods.
Can I use cross-quantilogram on non-stationary data?
No. The method assumes stationarity. If your series are I(1) or integrated, difference them first or test for cointegration relationships. Non-stationary data will yield spurious results.
How do I choose which quantile pairs to examine?
Start with the most economically meaningful pairs: (5%, 50%), (50%, 95%), or (5%, 95%) to study lower-tail, central, and upper-tail dependence. Then explore intermediate quantiles to map dependence across the full distribution. Domain knowledge should guide selection.
Sources
- 1.Linton, O., & Whang, Y. J. (2012). Quantile comparisons of time series data. Journal of Econometrics, 170(2), 242-257.
- 2.Kılıç, R., & Pohlmann, T. (2011). Directional spillover effects in international equity markets. Journal of Banking & Finance, 35(9), 2351-2361.
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Cite this page
ScholarGate. (2026, June 3). Cross-Quantilogram. ScholarGate. https://scholargate.app/econometrics/cross-quantilogram