Understanding Regressions with Observations Collected at High Frequency over Long Span
Yoosoon Chang (),
Ye Lu and
Joon Y. Park
No 2018-10, Working Papers from University of Sydney, School of Economics
In this paper, we analyze regressions with observations collected at small time interval over 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 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 longrun variance estimate. This is supported, strongly and unambiguously, by our empirical illustration.
Keywords: high frequency regression; spurious regression; continuous time model; asymptotics; longrun variance estimation (search for similar items in EconPapers)
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