Understanding Regressions with Observations Collected at High Frequency over Long Span

Yoosoon Chang (), Ye Lu () and Joon Park ()
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Yoosoon Chang: Indiana University, Department of Economics
Ye Lu: School of Economics, University of Sydney
Joon Park: Indiana University, Department of Economics

No 2025-001, CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

Abstract: 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 δ 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 δ → 0 sufficiently fast relative to T → ∞. Such a phenomenon is indeed what is frequently observedin practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robustversion 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.

Keywords: high frequency regression; spurious regression; continuous-time model; asymptotics; long-run variance estimation (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Pages: 62 pages
Date: 2025-01
New Economics Papers: this item is included in nep-ets
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