Testing for Jump Spillovers Without Testing for Jumps

Abstract

This paper develops statistical tools for testing conditional independence among the jump components of the daily quadratic variation, which we estimate using intraday data. To avoid sequential bias distortion, we do not pretest for the presence of jumps. If the null is true, our test statistic based on daily integrated jumps weakly converges to a Gaussian random variable if both assets have jumps. If instead at least one asset has no jumps, then the statistic approaches zero in probability. We show how to compute asymptotically valid bootstrap-based critical values that result in a consistent test with asymptotic size equal to or smaller than the nominal size. Empirically, we study jump linkages between US futures and equity index markets.We find not only strong evidence of jump cross-excitation between the SPDR exchange-traded fund and E-mini futures on the S&P 500 index, but also that integrated jumps in the E-mini futures during the overnight period carry relevant information.

Systemic Tail Risk: High-Frequency Measurement, Evidence and Implications

“…In this direction, see also Bandi and Renò (2016), Bandi and Renò (2016), Jacod and Todorov (2009), Jacod and Todorov (2010), Todorov and Tauchen (2011) and Jacod et al (2017), who study cojumps between jumps in prices and jumps in volatility process. Further, a large number of studies detect the arrivals of cojumps across different asset classes and markets, see e.g., Lahaye et al (2011), Evans (2011), Dungey and Hvozdyk (2012), Winkelmann et al (2016), Bibinger and Winkelmann (2015), Corradi et al (2020) and Aït-Sahalia and Xiu (2016).…”