Understanding regressions with observations collected at high frequency over long span

• 成果类型: Article
• 署名作者: Chang, Yoosoon; Lu, Ye; Park, Joon Y.
• 署名单位: Indiana University System; Indiana University Bloomington; University of Sydney
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2055
• 发表日期: 2025
• 页码: 405-457
• 关键词: High frequency regression; spurious regression; continuous time model; asymptotics; long-run variance estimation; C13; C22

摘要

In this paper, we analyze regressions with observations collected at small time intervals over a long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval delta shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as delta -> 0 sufficiently fast relative to T -> infinity. Such a phenomenon is indeed what is frequently observed in practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robust version of the Wald test with an appropriate long-run variance estimate. This is supported, strongly and unambiguously, by our empirical illustration using the regression of long-term on short-term interest rates.