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A nonparametric test for diurnal variation in spot correlation processes

Kim Christensen, Ulrich Hounyo, Zhi Liu

TL;DR

The study develops a nonparametric, diurnal-variation test for spot correlations using high-frequency, jump-robust covariation estimators and a functional CLT framework. The core idea is to isolate the diurnal component via normalization of intraday covariances and test whether the intraday correlation curve deviates from a constant nightly baseline; the null distribution is derived and implemented through HAC-based covariance estimation and simulation. Monte Carlo experiments show good size and power properties for realistic sample sizes, while an extensive empirical application to DJIA components and SPY reveals a robust, upward-sloping intraday correlation pattern, with macro news and earnings announcements measurably shaping the curve. The results have practical implications for risk management and hedging, illustrating substantial variance reductions when diurnal correlation is accounted for and suggesting a framework to incorporate conditioning information into intraday correlation analysis.

Abstract

The association between log-price increments of exchange-traded equities, as measured by their spot correlation estimated from high-frequency data, exhibits a pronounced upward-sloping and almost piecewise linear relationship at the intraday horizon. There is notably lower-on average less positive-correlation in the morning than in the afternoon. We develop a nonparametric testing procedure to detect such variation in a correlation process. The test statistic has a known distribution under the null hypothesis, whereas it diverges under the alternative. We run a Monte Carlo simulation to discover the finite sample properties of the test statistic, which are close to the large sample predictions, even for small sample sizes and realistic levels of diurnal variation. In an application, we implement the test on a high-frequency dataset covering the stock market over an extended period. The test leads to rejection of the null most of the time. This suggests diurnal variation in the correlation process is a nontrivial effect in practice. We show how conditioning information about macroeconomic news and corporate earnings announcements affect the intraday correlation curve.

A nonparametric test for diurnal variation in spot correlation processes

TL;DR

The study develops a nonparametric, diurnal-variation test for spot correlations using high-frequency, jump-robust covariation estimators and a functional CLT framework. The core idea is to isolate the diurnal component via normalization of intraday covariances and test whether the intraday correlation curve deviates from a constant nightly baseline; the null distribution is derived and implemented through HAC-based covariance estimation and simulation. Monte Carlo experiments show good size and power properties for realistic sample sizes, while an extensive empirical application to DJIA components and SPY reveals a robust, upward-sloping intraday correlation pattern, with macro news and earnings announcements measurably shaping the curve. The results have practical implications for risk management and hedging, illustrating substantial variance reductions when diurnal correlation is accounted for and suggesting a framework to incorporate conditioning information into intraday correlation analysis.

Abstract

The association between log-price increments of exchange-traded equities, as measured by their spot correlation estimated from high-frequency data, exhibits a pronounced upward-sloping and almost piecewise linear relationship at the intraday horizon. There is notably lower-on average less positive-correlation in the morning than in the afternoon. We develop a nonparametric testing procedure to detect such variation in a correlation process. The test statistic has a known distribution under the null hypothesis, whereas it diverges under the alternative. We run a Monte Carlo simulation to discover the finite sample properties of the test statistic, which are close to the large sample predictions, even for small sample sizes and realistic levels of diurnal variation. In an application, we implement the test on a high-frequency dataset covering the stock market over an extended period. The test leads to rejection of the null most of the time. This suggests diurnal variation in the correlation process is a nontrivial effect in practice. We show how conditioning information about macroeconomic news and corporate earnings announcements affect the intraday correlation curve.
Paper Structure (17 sections, 10 theorems, 123 equations, 4 figures)

This paper contains 17 sections, 10 theorems, 123 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theoretical setup
  3. Spot correlation estimator
  4. Testing procedure
  5. Test statistic
  6. Extensions
  7. Stochastic diurnal correlation
  8. Incorporating conditioning information
  9. Small sample comparisons
  10. Empirical application
  11. Data description
  12. The diurnal pattern in correlation
  13. Conditioning information
  14. Implications for risk management
  15. Conclusion
  16. ...and 2 more sections

Key Result

Theorem 3.1

Suppose that Assumptions (V), (J), and (C1) -- (C5) (with $q = 1$ in Assumption (C5)) hold. As $n \rightarrow \infty$, $T \rightarrow \infty$, $k_{n} \rightarrow \infty$ such that $k_{n} / n \rightarrow 0$, it holds that for $\tau \in [0,1]$, Moreover, where

Figures (4)

  • Figure 1: Illustration of stochastic correlation process.
  • Figure 2: A representative diurnal covariance and correlation function.
  • Figure 3: Conditional diurnal correlation function.
  • Figure 4: The distribution of the minimum variance hedge ratio.

Theorems & Definitions (10)

  • Theorem 3.1
  • Theorem 4.1
  • Theorem 4.2
  • Proposition 4.1
  • Theorem 4.3
  • Theorem 5.1
  • Theorem 5.2
  • Lemma A.1
  • Lemma A.2
  • Proposition A.1