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Discrete Fourier Transforms of Fractional Processes August

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  • Phillips, Peter

Abstract

Discrete Fourier transforms (dft's) of fractional processes are studied and a exact representation of the dft is given in terms of the component data. The new representation gives the frequency domain form of the model for a fractional process, and is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d > 1/2. Various asymptotic approximations are suggested. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested.

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  • Phillips, Peter, 1999. "Discrete Fourier Transforms of Fractional Processes August," Working Papers 149, Department of Economics, The University of Auckland.
    • Handle: RePEc:auc:wpaper:149
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    File URL: http://hdl.handle.net/2292/149
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    2. Bardet Jean-Marc & Dola Béchir, 2016. "Semiparametric Stationarity and Fractional Unit Roots Tests Based on Data-Driven Multidimensional Increment Ratio Statistics," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 115-153, July.
    3. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    4. Samet Günay, 2016. "Performance of the Multifractal Model of Asset Returns (MMAR): Evidence from Emerging Stock Markets," IJFS, MDPI, vol. 4(2), pages 1-17, May.
    5. Proelss, Juliane & Schweizer, Denis & Seiler, Volker, 2020. "The economic importance of rare earth elements volatility forecasts," International Review of Financial Analysis, Elsevier, vol. 71(C).
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    8. 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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    10. Magazzino, Cosimo & Mutascu, Mihai Ioan, 2022. "The Italian fiscal sustainability in a long-run perspective," The Journal of Economic Asymmetries, Elsevier, vol. 26(C).
    11. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    12. Esposti, Roberto, 2017. "What Makes Commodity Prices Move Together? An Answer From A Dynamic Factor Model," 2017 International Congress, August 28-September 1, 2017, Parma, Italy 260889, European Association of Agricultural Economists.
    13. Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    14. Goodell, John W. & McGroarty, Frank & Urquhart, Andrew, 2015. "Political uncertainty and the 2012 US presidential election: A cointegration study of prediction markets, polls and a stand-out expert," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 162-171.
    15. Ewa M. Syczewska, 2006. "The Phillips Method of Fractional Integration Parameter Estimation and Aggregation of PLN Exchange Rates," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 7, pages 209-220.
    16. Monge, Manuel & Cristóbal, Enrique, 2021. "Terrorism and the behavior of oil production and prices in OPEC," Resources Policy, Elsevier, vol. 74(C).
    17. Monge, Manuel & Gil-Alana, Luis A., 2021. "Lithium industry and the U.S. crude oil prices. A fractional cointegration VAR and a Continuous Wavelet Transform analysis," Resources Policy, Elsevier, vol. 72(C).
    18. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    19. Shi, Wendong & Sun, Jingwei, 2016. "Aggregation and long-memory: An analysis based on the discrete Fourier transform," Economic Modelling, Elsevier, vol. 53(C), pages 470-476.
    20. Leonardo Chaves Borges Cardoso & Maurício Vaz Lobo Bittencourt, 2016. "Price Volatility Transmission From Oil To Energy And Non-Energy Agricultural Commodities," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 181, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    21. Tan, Zhengxun & Liu, Juan & Chen, Juanjuan, 2021. "Detecting stock market turning points using wavelet leaders method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    22. Xiao-Ming Li, 2014. "Rethinking Long Memory and Structural Breaks in the Forward Premium," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(4), pages 455-485, September.
    23. Monge, Manuel, 2021. "U.S. historical initial jobless claims. Is it different with the coronavirus crisis? A fractional integration analysis," International Economics, Elsevier, vol. 167(C), pages 88-95.

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    Keywords

    Discrete Fourier transform; Economics;

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