IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v16y2025i2p405-457.html

Understanding regressions with observations collected at high frequency over long span

Author

Listed:
  • Yoosoon Chang
  • Ye Lu
  • Joon Y. Park

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 using the regression of long‐term on short‐term interest rates.

Suggested Citation

  • Yoosoon Chang & Ye Lu & Joon Y. Park, 2025. "Understanding regressions with observations collected at high frequency over long span," Quantitative Economics, Econometric Society, vol. 16(2), pages 405-457, May.
    • Handle: RePEc:wly:quante:v:16:y:2025:i:2:p:405-457
    DOI: 10.3982/QE2055
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE2055
    Download Restriction: no
    File URL: https://libkey.io/10.3982/QE2055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    3. Daniel L. Thornton, 2018. "Greenspan's Conundrum and the Fed's Ability to Affect Long‐Term Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(2-3), pages 513-543, March.
    4. Yoosoon Chang & Yongok Choi & Hwagyun Kim & Joon Y. Park, 2016. "Evaluating factor pricing models using high‐frequency panels," Quantitative Economics, Econometric Society, vol. 7(3), pages 889-933, November.
    5. 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.
    6. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2020. "Testing for Stationarity at High Frequency," Journal of Econometrics, Elsevier, vol. 215(2), pages 341-374.
    7. Lu, Ye & Park, Joon Y., 2019. "Estimation of longrun variance of continuous time stochastic process using discrete sample," Journal of Econometrics, Elsevier, vol. 210(2), pages 236-267.
    8. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    9. 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.
    10. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    11. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    12. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    13. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    14. Fama, Eugene F., 1984. "The information in the term structure," Journal of Financial Economics, Elsevier, vol. 13(4), pages 509-528, December.
    15. Ben S. Bernanke, 2020. "The New Tools of Monetary Policy," American Economic Review, American Economic Association, vol. 110(4), pages 943-983, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2020. "Testing for Stationarity at High Frequency," Journal of Econometrics, Elsevier, vol. 215(2), pages 341-374.
    3. Pellatt, Daniel F. & Sun, Yixiao, 2023. "Asymptotic F test in regressions with observations collected at high frequency over long span," Journal of Econometrics, Elsevier, vol. 235(2), pages 1281-1309.
    4. Hwang, Taeyoon & Vogelsang, Timothy J., 2024. "Some fixed-b results for regressions with high frequency data over long spans," Journal of Econometrics, Elsevier, vol. 244(2).
    5. Chang, Yoosoon & Lu, Ye & Park, Joon Y., 2018. "Understanding Regressions with Observations Collected at High Frequency over Long Span," Working Papers 2018-10, University of Sydney, School of Economics.
    6. Getu Hailu & Alex Maynard & Alfons Weersink, 2015. "Empirical analysis of corn and soybean basis in Canada," Applied Economics, Taylor & Francis Journals, vol. 47(51), pages 5491-5509, November.
    7. Christensen, Kim & Oomen, Roel & Renò, Roberto, 2022. "The drift burst hypothesis," Journal of Econometrics, Elsevier, vol. 227(2), pages 461-497.
    8. Irine Tahjiba Angela, 2026. "Global economic policy uncertainty and credit risk in emerging economies: evidence from Bangladesh," Future Business Journal, Springer, vol. 12(1), pages 1-32, December.
    9. Karsten Reichold, 2022. "A Residuals-Based Nonparametric Variance Ratio Test for Cointegration," Papers 2211.06288, arXiv.org, revised Dec 2022.
    10. Ekaterini Panopoulou, 2005. "A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators," The Institute for International Integration Studies Discussion Paper Series iiisdp067, IIIS.
    11. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    12. Pär Österholm, 2005. "The Taylor Rule: A Spurious Regression?," Bulletin of Economic Research, Wiley Blackwell, vol. 57(3), pages 217-247, July.
    13. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    14. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    15. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    16. Carrasco, Marine & Kotchoni, Rachidi, 2017. "Efficient Estimation Using The Characteristic Function," Econometric Theory, Cambridge University Press, vol. 33(2), pages 479-526, April.
    17. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
    18. Henryk Gurgul & Lukaz Lach & Tomasz Wojtowicz, 2016. "Impact of US Macroeconomic News Announcements on Intraday Causalities on Selected European Stock Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 66(5), pages 405-425, October.
    19. Kent Wang, 2009. "Volatility linkages of the equity, bond and money markets: an implied volatility approach," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 49(1), pages 207-219, March.
    20. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:quante:v:16:y:2025:i:2:p:405-457. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.