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Understanding Regressions with Observations Collected at High Frequency over Long Span

Author

Listed:
  • Yoosoon Chang

    (Indiana University, Department of Economics)

  • Ye Lu

    (School of Economics, University of Sydney)

  • Joon Park

    (Indiana University, Department of Economics)

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.

Suggested Citation

  • Yoosoon Chang & Ye Lu & Joon Park, 2025. "Understanding Regressions with Observations Collected at High Frequency over Long Span," CAEPR Working Papers 2025-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2025001
    as

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    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2025-001.pdf
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    References listed on IDEAS

    as
    1. Kim, Jihyun & Park, Joon Y., 2017. "Asymptotics for recurrent diffusions with application to high frequency regression," Journal of Econometrics, Elsevier, vol. 196(1), pages 37-54.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    high frequency regression; spurious regression; continuous-time model; asymptotics; long-run variance estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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