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Low-Frequency Econometrics

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  • Ulrich K. Müller
  • Mark W. Watson

Abstract

Many questions in economics involve long-run or trend variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of low-frequency trigonometric weighted averages, which in turn can be used to conduct inference about long-run variability and covariability. Because the low-frequency weighted averages have large sample normal distributions, large sample valid inference can often be conducted using familiar small sample normal inference procedures. Moreover, the general approach is applicable for a wide range of persistent stochastic processes that go beyond the familiar I(0) and I(1) models.

Suggested Citation

  • Ulrich K. Müller & Mark W. Watson, 2015. "Low-Frequency Econometrics," NBER Working Papers 21564, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:21564
    Note: TWP
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    References listed on IDEAS

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    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
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    9. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
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    2. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    3. Kevin Hjortshøj O'Rourke, 2015. "Economic Impossibilities for our Grandchildren?," NBER Working Papers 21807, National Bureau of Economic Research, Inc.
    4. Galstyan, Vahagn, 2023. "Understanding the Joint Dynamics of Inflation and Wage Growth in the Euro Area," Research Technical Papers 11/RT/23, Central Bank of Ireland.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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