IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v102y2017icp456-466.html
   My bibliography  Save this article

Identification and validation of stable ARFIMA processes with application to UMTS data

Author

Listed:
  • Burnecki, Krzysztof
  • Sikora, Grzegorz

Abstract

In this paper we present an identification and validation scheme for stable autoregressive fractionally integrated moving average (ARFIMA) time series. The identification part relies on a recently introduced estimator which is a generalization of that of Kokoszka and Taqqu and a new fractional differencing algorithm. It also incorporates a low-variance estimator for the memory parameter based on the sample mean-squared displacement. The validation part includes standard noise diagnostics and backtesting procedure. The scheme is illustrated on Universal Mobile Telecommunications System (UMTS) data collected in an urban area. We show that the stochastic component of the data can be modeled by the long memory ARFIMA. This can help to monitor possible hazards related to the electromagnetic radiation.

Suggested Citation

  • Burnecki, Krzysztof & Sikora, Grzegorz, 2017. "Identification and validation of stable ARFIMA processes with application to UMTS data," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 456-466.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:456-466
    DOI: 10.1016/j.chaos.2017.03.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917301200
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.03.059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    2. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    3. Souza, Sergio R. & Tabak, Benjamin M. & Cajueiro, Daniel O., 2008. "Long memory testing for Fed Funds Futures’ contracts," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 180-186.
    4. Li, Hui & Wu, Min & Wang, Xiao-Tian, 2009. "Fractional-moment Capital Asset Pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 412-421.
    5. Xiu, Jin & Jin, Yao, 2007. "Empirical study of ARFIMA model based on fractional differencing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 138-154.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Barkoulas, John T. & Barilla, Anthony G. & Wells, William, 2016. "Long-memory exchange rate dynamics in the euro era," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 92-100.
    8. Cajueiro, Daniel O. & Tabak, Benjamin M., 2009. "Testing for long-range dependence in the Brazilian term structure of interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1559-1573.
    9. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    10. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    11. Burnecki, Krzysztof & Gajda, Janusz & Sikora, Grzegorz, 2011. "Stability and lack of memory of the returns of the Hang Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3136-3146.
    12. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Time-varying long-range dependence in US interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 360-367.
    13. David W. Sims & Emily J. Southall & Nicolas E. Humphries & Graeme C. Hays & Corey J. A. Bradshaw & Jonathan W. Pitchford & Alex James & Mohammed Z. Ahmed & Andrew S. Brierley & Mark A. Hindell & David, 2008. "Scaling laws of marine predator search behaviour," Nature, Nature, vol. 451(7182), pages 1098-1102, February.
    14. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    15. Joelson, Maminirina & Golder, Jacques & Beltrame, Philippe & Néel, Marie-Christine & Di Pietro, Liliana, 2016. "On fractal nature of groundwater level fluctuations due to rainfall process," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 103-115.
    16. Krzysztof Burnecki & Agnieszka Wylomanska & Aleksei Chechkin, 2015. "Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-23, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Adriana AnaMaria Davidescu & Simona-Andreea Apostu & Aurel Marin, 2021. "Forecasting the Romanian Unemployment Rate in Time of Health Crisis—A Univariate vs. Multivariate Time Series Approach," IJERPH, MDPI, vol. 18(21), pages 1-31, October.
    2. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    4. Paweł D. Domański, 2024. "Energy-Aware Multicriteria Control Performance Assessment," Energies, MDPI, vol. 17(5), pages 1-18, March.
    5. Vygintas Gontis, 2023. "Discrete $q$-exponential limit order cancellation time distribution," Papers 2306.00093, arXiv.org, revised Oct 2023.
    6. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    7. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Carlos D. Ramirez, 2024. "The effect of economic policy uncertainty under fractional integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 89-110, January.
    3. Elkin Castaño & Santiago Gallón & Karoll Gómez, 2010. "Estimation Biases, Size and Power of a Test on the Long Memory Parameter in ARFIMA Models," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 73, pages 131-148.
    4. Bhandari, Avishek, 2020. "Long memory and fractality among global equity markets: A multivariate wavelet approach," MPRA Paper 99653, University Library of Munich, Germany.
    5. S. Lardic & V. Mignon, 2002. "Term premium and long-range dependence in volatility : A FIGARCH-M estimation on some Asian countries," THEMA Working Papers 2002-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Mr. Jun Nagayasu, 2003. "The Efficiency of the Japanese Equity Market," IMF Working Papers 2003/142, International Monetary Fund.
    7. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    8. Wang, Xiao-Tian & Yan, Hai-Gang & Tang, Ming-Ming & Zhu, En-Hui, 2010. "Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 452-458.
    9. Henryk Gurgul & Tomasz Wójtowicz, 2006. "Long-run properties of trading volume and volatility of equities listed in DJIA index," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(3-4), pages 29-56.
    10. Pınar Kaya Soylu & Mustafa Okur & Özgür Çatıkkaş & Z. Ayca Altintig, 2020. "Long Memory in the Volatility of Selected Cryptocurrencies: Bitcoin, Ethereum and Ripple," JRFM, MDPI, vol. 13(6), pages 1-21, May.
    11. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    12. Assaf, Ata & Bhandari, Avishek & Charif, Husni & Demir, Ender, 2022. "Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19," International Review of Financial Analysis, Elsevier, vol. 82(C).
    13. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    14. Margherita Gerolimetto & Stefano Magrini, 2020. "Testing for boundary conditions in case of fractionally integrated processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 357-371, June.
    15. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    16. Kim Liow, 2009. "Long-term Memory in Volatility: Some Evidence from International Securitized Real Estate Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 39(4), pages 415-438, November.
    17. Salisu, Afees A. & Ndako, Umar B. & Adediran, Idris A. & Swaray, Raymond, 2020. "A fractional cointegration VAR analysis of Islamic stocks: A global perspective," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    18. Castano Vélez, Elkin & Gallón Gómez, Santiago Alejandro & Gómez Portilla, Karoll, 2011. "Sesgos en estimación, tamano y potencia de una prueba sobre el parámetro de memoria larga en modelos ARFIMA," Revista Lecturas de Economía, Universidad de Antioquia, CIE, February.
    19. Alexander Ayertey Odonkor & Emmanuel Nkrumah Ababio & Emmanuel Amoah- Darkwah & Richard Andoh, 2022. "Stock Returns and Long-range Dependence," Global Business Review, International Management Institute, vol. 23(1), pages 37-47, February.
    20. Matti Vir, 2000. "Analysing long memory and asymmetries," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 240-258.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:456-466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.