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Using Double Frequency in Fourier Dickey–Fuller Unit Root Test

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  • Yifei Cai

    (University of Western Australia)

  • Tolga Omay

    (Atilim University)

Abstract

We propose a double frequency fourier Dickey–Fuller (DF) unit root test. The asymptotic theory of the newly proposed test is first presented in this study. We conduct a series of simulations which suggest the proposed test statistic has correct size performance and gains more power when breaks are located at the beginning and end of the sample and in smooth type. In empirical analysis, we utilize the new test to examine the unit root hypothesis of relative commodity prices measured by Harvey et al. (Rev Econ Stat 92(2):367–377, 2010). The empirical results show that more relative commodity prices are stationary around a deterministic trend generated from double frequency Fourier function.

Suggested Citation

  • Yifei Cai & Tolga Omay, 2022. "Using Double Frequency in Fourier Dickey–Fuller Unit Root Test," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 445-470, February.
    • Handle: RePEc:kap:compec:v:59:y:2022:i:2:d:10.1007_s10614-020-10075-5
    DOI: 10.1007/s10614-020-10075-5
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    Cited by:

    1. Tolga Omay & Aysegul Corakci & Esra Hasdemir, 2021. "High Persistence and Nonlinear Behavior in Financial Variables: A More Powerful Unit Root Testing in the ESTAR Framework," Mathematics, MDPI, vol. 9(20), pages 1-21, October.
    2. Furkan Emirmahmutoglu & Tolga Omay & Syed Jawad Hussain Shahzad & Safwan Mohd Nor, 2021. "Smooth Break Detection and De-Trending in Unit Root Testing," Mathematics, MDPI, vol. 9(4), pages 1-25, February.
    3. Yifei Cai & Jamel Saadaoui, 2022. "Fourier DF unit root test for R&D intensity of G7 countries," Applied Economics, Taylor & Francis Journals, vol. 54(42), pages 4900-4914, September.
    4. Omay, Tolga & Shahbaz, Muhammad & Stewart, Chris, 2021. "Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test," MPRA Paper 107691, University Library of Munich, Germany, revised 10 May 2021.
    5. Jamel Saadaoui & Marco Chi Keung Lau & Yifei Cai, 2022. "Assessing Debt Stationarity and Sustainability in the Longer Run with Fourier DF Unit Root Tests and Time-Varying Fiscal Reaction Functions," Working Papers of BETA 2022-11, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.

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