Hiemstra-Jones Nonlinear Granger Causality Test
Also known as: HJ Nonlinear Causality Test, Hiemstra-Jones Test, Nonlinear Granger Causality (Hiemstra-Jones), HJ Nedensellik Testi
The Hiemstra-Jones test, introduced in 1994, is a nonparametric procedure for detecting nonlinear causal relationships between two time series after removing their linear interdependencies. Developed in the context of stock price and trading volume dynamics, it extends the standard linear Granger causality framework by using correlation integral statistics to detect predictability arising from nonlinear mechanisms that linear VAR models cannot capture.
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When to use it
The Hiemstra-Jones test is appropriate when standard linear Granger causality tests are inconclusive or when theory suggests nonlinear dynamics—common in financial markets, macroeconomic regimes, or ecological systems. It requires stationary, prewhitened residuals; therefore both series should be filtered or differenced to achieve stationarity before application. Key limitations include sensitivity to the choice of embedding dimension m and bandwidth epsilon, and the test may over-reject in finite samples with strong conditional heteroskedasticity. When nonlinear causality is suspected but volatility clustering is prominent, the Diks-Panchenko (2006) modification is often preferred as a bias-corrected alternative.
Strengths & limitations
- Detects nonlinear causal linkages that linear Granger causality tests cannot identify
- Nonparametric approach requires no distributional assumptions about the data-generating process
- Widely applied and replicated benchmark for nonlinear causality in financial econometrics
- Simple to implement after VAR prewhitening using standard correlation integral estimators
- Results can be sensitive to the choice of embedding dimension and bandwidth epsilon, which have no universally optimal selection rules
- May over-reject the null (size distortion) in the presence of ARCH/GARCH-type conditional heteroskedasticity
- Requires adequate sample sizes for reliable asymptotic approximations; small samples reduce power
- Only tests for causality in mean; nonlinear causality in higher moments (e.g., volatility) requires separate procedures
Frequently asked
How does the Hiemstra-Jones test differ from standard Granger causality?
Standard Granger causality operates within a linear VAR framework and detects only linear predictive relationships. The Hiemstra-Jones test first removes all linear dependence via VAR prewhitening and then applies a nonparametric correlation-integral statistic to the residuals, specifically targeting nonlinear causal relationships that survive after linear effects are partialled out.
Why might I prefer the Diks-Panchenko test over Hiemstra-Jones?
Diks and Panchenko (2006) showed that the Hiemstra-Jones statistic can over-reject the null hypothesis in finite samples even when no causality is present, particularly under conditional heteroskedasticity. Their modified test corrects this size distortion by using a different normalization, making it more reliable in practice, especially with financial time series exhibiting volatility clustering.
How should I choose the embedding dimension and bandwidth for the test?
There is no single optimal rule, but common practice is to set epsilon between 0.5 and 1.5 times the series standard deviation and try embedding dimensions from 1 to 5. Robustness of results across a range of parameter combinations strengthens confidence in the conclusion. Reporting sensitivity to these choices is considered good empirical practice.
Sources
- Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price-volume relation. The Journal of Finance, 49(5), 1639–1664. DOI: 10.1111/j.1540-6261.1994.tb04776.x ↗
How to cite this page
ScholarGate. (2026, June 2). Hiemstra-Jones Nonlinear Granger Causality Test. ScholarGate. https://scholargate.app/en/econometrics/hiemstra-jones-causality
Which method?
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