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Testing Models of Low-Frequency Variability

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  • Ulrich K. Müller
  • Mark W. Watson

Abstract

We develop a framework to assess how successfully standard time series models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle. Copyright 2008 The Econometric Society.

Suggested Citation

  • Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
  • Handle: RePEc:ecm:emetrp:v:76:y:2008:i:5:p:979-1016
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    Cited by:

    1. Alfred A. Haug, 2014. "On real interest rate persistence: the role of breaks," Applied Economics, Taylor & Francis Journals, vol. 46(10), pages 1058-1066, April.
    2. Zhongjun Qu, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 423-438, July.
    3. Gonzalo, Jesús & Gadea Rivas, María Dolores, 2017. "Trends in distributional characteristics : Existence of global warming," UC3M Working papers. Economics 24121, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Ulrich K. Müller & Mark W. Watson, 2015. "Low-Frequency Econometrics," NBER Working Papers 21564, National Bureau of Economic Research, Inc.
    5. Bandi, F.M & Perron, B & Tamoni, Andrea & Tebaldi, C., 2017. "The scale of predictability," LSE Research Online Documents on Economics 85646, London School of Economics and Political Science, LSE Library.
    6. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    7. Ulrich Mueller & Mark W. Watson, 2013. "Measuring Uncertainty about Long-Run Prediction," NBER Working Papers 18870, National Bureau of Economic Research, Inc.
    8. repec:eee:econom:v:204:y:2018:i:1:p:54-65 is not listed on IDEAS
    9. Alfred A. Haug & William G. Dewald, 2012. "Money, Output, And Inflation In The Longer Term: Major Industrial Countries, 1880–2001," Economic Inquiry, Western Economic Association International, vol. 50(3), pages 773-787, July.
    10. Zhou, Bo, 2017. "Semiparametric inference for non-LAN models," Other publications TiSEM 0ea4fd8a-937d-4c19-8f77-f, Tilburg University, School of Economics and Management.
    11. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    12. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    13. Giannone, Domenico & Lenza, Michele & Primiceri, Giorgio E, 2016. "Priors for the Long Run," CEPR Discussion Papers 11261, C.E.P.R. Discussion Papers.
    14. Cuestas Juan Carlos & Gil-Alana Luis Alberiko, 2016. "Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 57-74, February.
    15. Arturo Estrella, 2007. "Extracting business cycle fluctuations: what do time series filters really do?," Staff Reports 289, Federal Reserve Bank of New York.
    16. Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(01), pages 60-93, February.
    17. Onatski, Alexei & Uhlig, Harald, 2012. "Unit Roots In White Noise," Econometric Theory, Cambridge University Press, vol. 28(03), pages 485-508, June.
    18. Francesco Bianchi & Martin Lettau & Sydney C. Ludvigson, 2016. "Monetary Policy and Asset Valuation," NBER Working Papers 22572, National Bureau of Economic Research, Inc.
    19. Haug, Alfred A. & King, Ian, 2014. "In the long run, US unemployment follows inflation like a faithful dog," Journal of Macroeconomics, Elsevier, vol. 41(C), pages 42-52.
    20. Federico M. Bandi & Bernard Perron & Andrea Tamoni & Claudio Tebaldi, 2014. "The scale of predictability," Working Papers 509, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    21. White Halbert & Granger Clive W.J., 2011. "Consideration of Trends in Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-40, February.
    22. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    23. Sizova, Natalia, 2014. "A frequency-domain alternative to long-horizon regressions with application to return predictability," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 261-272.
    24. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    25. Charles S. Bos & Siem Jan Koopman & Marius Ooms, 2007. "Long memory modelling of inflation with stochastic variance and structural breaks," CREATES Research Papers 2007-44, Department of Economics and Business Economics, Aarhus University.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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