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Testing fractional unit roots with non-linear smooth break approximations using Fourier functions

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  • Luis A. Gil-Alana
  • OlaOluwa S. Yaya

Abstract

In this paper, we present a testing procedure for fractional orders of integration in the context of non-linear terms approximated by Fourier functions. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper.

Suggested Citation

  • Luis A. Gil-Alana & OlaOluwa S. Yaya, 2021. "Testing fractional unit roots with non-linear smooth break approximations using Fourier functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(13-15), pages 2542-2559, November.
    • Handle: RePEc:taf:japsta:v:48:y:2021:i:13-15:p:2542-2559
    DOI: 10.1080/02664763.2020.1757047
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    Cited by:

    1. OlaOluwa S. Yaya & Ahamuefula E. Ogbonna & Robert Mudida & Nuruddeen Abu, 2021. "Market efficiency and volatility persistence of cryptocurrency during pre‐ and post‐crash periods of Bitcoin: Evidence based on fractional integration," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1318-1335, January.
    2. Juan Carlos Cuestas & Luis A. Gil-Alana, 2022. "Unemployment hysteresis by sex and education attainment in the EU," Working Papers 2022/06, Economics Department, Universitat Jaume I, Castellón (Spain).
    3. Martin-Valmayor, Miguel A. & Gil-Alana, Luis A. & Infante, Juan, 2023. "Energy prices in Europe. Evidence of persistence across markets," Resources Policy, Elsevier, vol. 82(C).
    4. Caporale, Guglielmo Maria & Gil-Alana, Luis Alberiko & Puertolas, Francisco, 2024. "Modelling profitability of private equity: A fractional integration approach," Research in International Business and Finance, Elsevier, vol. 67(PA).
    5. Yener, Coskun & Akinsomi, Omokolade & Gil-Alana, Luis A. & Yaya, OlaOluwa S, 2023. "Stock Market Responses to COVID-19: The Behaviors of Mean Reversion, Dependence and Persistence," MPRA Paper 117002, University Library of Munich, Germany.
    6. Luis A. Gil-Alana & Sakiru Adebola Solarin & Mehmet Balcilar & Rangan Gupta, 2023. "Productivity and GDP: international evidence of persistence and trends over 130 years of data," Empirical Economics, Springer, vol. 64(3), pages 1219-1246, March.
    7. Sakiru Adebola Solarin & Gema Lopez & Luis A. Gil‐Alana, 2022. "Persistence analysis of research intensity in OECD countries since 1870," Australian Economic Papers, Wiley Blackwell, vol. 61(4), pages 738-750, December.
    8. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2023. "U.S. House Prices by Census Division: Persistence, Trends and Structural Breaks," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 29(1), pages 79-90, May.
    9. Martin-Valmayor, Miguel A. & Gil-Alana, Luis A. & Martín, Asís Pardo, 2023. "US biofuel market persistence and mean reversion properties," Economic Analysis and Policy, Elsevier, vol. 78(C), pages 648-660.
    10. Raquel Ayestarán & Juan Infante & Juan José Tenorio & Luis Alberiko Gil-Alana, 2023. "Evidence of Inflation Using Harmonized Consumer Price Indices in Some Euro Countries: France, Germany, Italy, and Spain, along with the Euro Zone," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    11. OlaOluwa S.Yaya & Pui Kiew Ling & Fumitaka Furuoka & Chinyere Mary Rose Ezeoke & Ray Ikechukwu Jacob, 2019. "Can West African countries catch up with Nigeria? Evidence from smooth nonlinearity method in fractional unit root framework," International Economics, CEPII research center, issue 158, pages 51-63.
    12. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2023. "Nominal and real wages in the UK, 1750–2015: mean reversion, persistence and structural breaks," SN Business & Economics, Springer, vol. 3(8), pages 1-10, August.
    13. Sakiru Adebola Solarin & Lorenzo Bermejo & Luis Gil-Alana, 2023. "Testing persistence of ammonia emissions using historical data of more than two centuries in OECD countries," Environment Systems and Decisions, Springer, vol. 43(3), pages 379-392, September.
    14. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana & Carlos Poza, 2022. "Inflation in the G7 countries: persistence and structural breaks," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 46(3), pages 493-506, July.
    15. Claudio-Quiroga, Gloria & Gil-Alana, Luis A. & Maiza-Larrarte, Andoni, 2023. "Mineral prices persistence and the development of a new energy vehicle industry in China: A fractional integration approach," Resources Policy, Elsevier, vol. 82(C).
    16. Gil-Alana, Luis A. & Infante, Juan & Martín-Valmayor, Miguel Angel, 2023. "Persistence and long run co-movements across stock market prices," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 347-357.
    17. Yaya, OlaOluwa S. & Vo, Xuan Vinh, 2021. "Testing day-of-the-week persistence and seasonality in Spanish Electricity Energy prices," MPRA Paper 112652, University Library of Munich, Germany, revised 03 Apr 2022.
    18. Guglielmo Maria Caporale & Luis A. Gil-Alana & OlaOluwa Simon Yaya, 2022. "Modelling Persistence and Non-Linearities in the US Treasury 10-Year Bond Yields," CESifo Working Paper Series 9554, CESifo.
    19. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2023. "Long-Run Trends and Cycles in US House Prices," CESifo Working Paper Series 10751, CESifo.
    20. Luis Alberiko Gil-Alana & Francisco Puertolas-Montanes, 2023. "Profitability of private equity: mean reversion and transitory shocks," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 47(2), pages 458-471, June.
    21. Yaya, OlaOluwa S & Ogbonna, Ephraim A & Furuoka, Fumitaka & Gil-Alana, Luis A., 2019. "A new unit root analysis for testing hysteresis in unemployment," MPRA Paper 96621, University Library of Munich, Germany.
    22. Sakiru, Solarin Adebola & Gil-Alana, Luis A. & Gonzalez-Blanch, Maria Jesus, 2022. "Persistence of economic complexity in OECD countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    23. Monge, Manuel & Romero Rojo, María Fátima & Gil-Alana, Luis Alberiko, 2023. "The impact of geopolitical risk on the behavior of oil prices and freight rates," Energy, Elsevier, vol. 269(C).

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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