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

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  • 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.

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  • 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
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    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. 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.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Li, Hui & Wu, Min & Wang, Xiao-Tian, 2009. "Fractional-moment Capital Asset Pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 412-421.
    12. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    13. 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.
    14. 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.
    15. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    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.
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