Deviations of asset prices from the random walk dynamic imply the predictability of asset returns and thus have important implications for portfolio construction and risk management. This paper proposes a real-time monitoring device for such deviations using intraday high-frequency data. The proposed procedures are based on unit root tests with in-fill asymptotics but extended to take the empirical features of high-frequency financial data (particularly jumps) into consideration. We derive the limiting distributions of the tests under both the null hypothesis of a random walk with jumps and the alternative of mean reversion/explosiveness with jumps. The limiting results show that ignoring the presence of jumps could potentially lead to severe size distortions of both the standard left-sided (against mean reversion) and right-sided (against explosiveness) unit root tests. The simulation results reveal satisfactory performance of the proposed tests even with data from a relatively short time span. As an illustration, we apply the procedure to the Nasdaq composite index at the 10-minute frequency over two periods: around the peak of the dot-com bubble and during the 2015–2106 stock market sell-off. We find strong evidence of explosiveness in asset prices in late 1999 and mean reversion in late 2015. We also show that accounting for jumps when testing the random walk hypothesis on intraday data is empirically relevant and that ignoring jumps can lead to different conclusions.

中文翻译：

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高频数据的单元根测试

资产价格与随机游走动态的偏差意味着资产回报的可预测性，因此对投资组合构建和风险管理具有重要意义。本文提出了一种利用日内高频数据对此类偏差进行实时监测的装置。所提出的程序基于具有填充渐近线的单位根检验，但扩展到考虑高频金融数据（特别是跳跃）的经验特征。我们在随机游走与跳跃的零假设和均值回归/爆炸性与跳跃的替代方案下得出了检验的极限分布。限制性结果表明，忽略跳跃的存在可能会导致标准左侧（反对均值回归）和右侧（反对爆炸性）单位根检验的严重尺寸扭曲。仿真结果表明，即使使用相对较短时间跨度的数据，所提出的测试也具有令人满意的性能。作为说明，我们在两个时期内以 10 分钟的频率将该程序应用于纳斯达克综合指数：互联网泡沫高峰期和 2015-2106 年股市抛售期间。我们发现了 1999 年末资产价格爆炸性和 2015 年末均值回归的有力证据。我们还表明，在对日内数据测试随机游走假设时考虑跳跃在经验上是相关的，并且忽略跳跃会导致不同的结论。