Asymptotic F test in regressions with observations collected at high frequency over long span

Daniel F. Pellatt and Yixiao Sun

Journal of Econometrics, 2023, vol. 235, issue 2, 1281-1309

Abstract: This paper proposes tests of linear hypotheses when the variables may be continuous-time processes with observations collected at a high sampling frequency over a long span. Utilizing series long run variance (LRV) estimation in place of the traditional kernel LRV estimation, we develop easy-to-implement and more accurate F tests in both stationary and nonstationary environments. The nonstationary environment accommodates exogenous regressors that are general semimartingales. Endogenous regressors are allowed in a nonstationary environment similar to cointegration models in the usual discrete-time setting. The F tests can be implemented in exactly the same way as in the discrete-time setting. The F tests are, therefore, robust to the continuous-time or discrete-time nature of the data. Simulations demonstrate the improved size accuracy and competitive power of the F tests relative to existing continuous-time testing procedures and their improved versions. The F tests are of practical interest as recent work by Chang et al. (2021) demonstrates that traditional inference methods can become invalid and produce spurious results when continuous-time processes are observed on finer grids over a long span.

Keywords: Continuous time model; F distribution; High-frequency regression; Long run variance estimation (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:2:p:1281-1309

DOI: 10.1016/j.jeconom.2022.10.007

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