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Comparison of optimization algorithms for selecting the fractional frequency in Fourier form unit root tests

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  • Tolga Omay
  • Furkan Emirmahmutoglu
  • Syed Jawad Hussain Shahzad

Abstract

We compare the performance of unit root tests which include flexible Fourier trends in their testing processes. The algorithms considered are those of Broyden, Fletcher, Goldfarb and Shanno (BFGS), Berndt, Hall, Hall and Hausman (BHHH), Simplex, Genetic and grid search (GS). The simulation results indicate that derivative-free methods, such as Genetic and Simplex, have advantages over hill-climbing methods, such as BFGS and BHHH in providing accurate fractional frequencies for fractional frequency flexible Fourier form (FFFFF) unit root test. When the parameters are estimated under the alternative hypothesis of the FFFFF type of unit root test, the grid search and derivative-free methods provide unbiased and efficient estimations. We also provide the asymptotic distribution of the FFFFF unit root test. We extend the FFFFF unit root test to a panel version in order to increase the power of the test. Finally, the empirical analyses of Covid19 unit root test show that derivative-free methods, are better than other methods. However, for big data and accurate estimation of the frequency parameters, the Simplex methodology using the bootstrap process is preferred.

Suggested Citation

  • Tolga Omay & Furkan Emirmahmutoglu & Syed Jawad Hussain Shahzad, 2021. "Comparison of optimization algorithms for selecting the fractional frequency in Fourier form unit root tests," Applied Economics, Taylor & Francis Journals, vol. 53(7), pages 761-780, February.
    • Handle: RePEc:taf:applec:v:53:y:2021:i:7:p:761-780
    DOI: 10.1080/00036846.2020.1814945
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    Cited by:

    1. Abbas, Hafiz Syed Mohsin & Xu, Xiaodong & Sun, Chunxia, 2022. "The role of state capacity and socio-economic determinants on health quality and its access in Pakistan (1990–2019)," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    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. Tolga Omay & Perihan Iren, 2023. "Controlling Heterogeneous Structure of Smooth Breaks in Panel Unit Root and Cointegration Testing," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 233-265, January.
    4. Tolga Omay & Muhammad Shahbaz & Chris Stewart, 2021. "Is there really hysteresis in the OECD unemployment rates? New evidence using a Fourier panel unit root test," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 48(4), pages 875-901, November.
    5. 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.

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