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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 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.

Suggested Citation

  • Yoosoon Chang & Ye Lu & Joon Park, 2019. "Understanding Regressions with Observations Collected at High Frequency over Long Span," CAEPR Working Papers 2019-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2019001
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    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2019-001.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. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. 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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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Papers of the Moment
      by Francis Diebold in No Hesitations on 2019-01-07 13:50:00

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    Cited by:

    1. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2020. "Testing for Stationarity at High Frequency," Journal of Econometrics, Elsevier, vol. 215(2), pages 341-374.
    2. Pellatt , Daniel & Sun, Yixiao, 2020. "Asymptotic F test in Regressions with Observations Collected at High Frequency over Long Span," University of California at San Diego, Economics Working Paper Series qt19f0d9wz, Department of Economics, UC San Diego.

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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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