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A Measure of Early Warning of Exchange-Rate Crises Based on the Hurst Coefficient and the Αlpha-Stable Parameter

Author

Listed:
  • Rodríguez-Aguilar, Román
  • Cruz-Aké, Salvador
  • Venegas-Martínez, Francisco

Abstract

The Hurst coefficient and the alpha-stable parameter are useful indicators in the analysis of time series to detect normality and absence of self-similarity. In particular, when these two features met simultaneously, it is said that the series is driven by white noise. This paper is aimed at developing an index to measure the degree to which a time series departs from white noise. The proposed index is built by using the principal component analysis of the Mahalanobis distances between the Hurst coefficient and the alpha-stable parameter from theoretical values of normality and absence of self-similarity. A zero value of the index corresponds to a pure white noise process, while a 100 value correspond to the maximum distance between the actual series and the theoretical white noise. The proposed index is applied to examine the exchange rate of the Mexican peso against the USA dollar. When examining the exchange rate, one distinctive finding of the Index is that it can be used as an early warning indicator of crises, as it is shown for the Mexican case.

Suggested Citation

  • Rodríguez-Aguilar, Román & Cruz-Aké, Salvador & Venegas-Martínez, Francisco, 2014. "A Measure of Early Warning of Exchange-Rate Crises Based on the Hurst Coefficient and the Αlpha-Stable Parameter," MPRA Paper 59046, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:59046
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    References listed on IDEAS

    as
    1. Refet S. Gürkaynak, 2008. "Econometric Tests Of Asset Price Bubbles: Taking Stock," Journal of Economic Surveys, Wiley Blackwell, vol. 22(1), pages 166-186, February.
    2. Christopher J. Neely, 2001. "The practice of central bank intervention: looking under the hood," Review, Federal Reserve Bank of St. Louis, vol. 83(May), pages 1-10.
    3. repec:crs:wpaper:9607 is not listed on IDEAS
    4. Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2012. "Leverage causes fat tails and clustered volatility," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 695-707, February.
    5. Mensi, Walid & Hammoudeh, Shawkat & Yoon, Seong-Min, 2014. "Structural breaks and long memory in modeling and forecasting volatility of foreign exchange markets of oil exporters: The importance of scheduled and unscheduled news announcements," International Review of Economics & Finance, Elsevier, vol. 30(C), pages 101-119.
    6. Fatum, Rasmus & Pedersen, Jesper & Sørensen, Peter Norman, 2013. "The intraday effects of central bank intervention on exchange rate spreads," Journal of International Money and Finance, Elsevier, vol. 33(C), pages 103-117.
    7. Kirchler, Michael & Huber, Jurgen, 2007. "Fat tails and volatility clustering in experimental asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1844-1874, June.
    8. Ansgar Belke & Gunther Schnabl, 2013. "Four Generations of Global Imbalances," Review of International Economics, Wiley Blackwell, vol. 21(1), pages 1-5, February.
    9. Jack Meaning & Feng Zhu, 2011. "The impact of recent central bank asset purchase programmes," BIS Quarterly Review, Bank for International Settlements, December.
    10. Jia, Zhanliang & Cui, Meilan & Li, Handong, 2012. "Research on the relationship between the multifractality and long memory of realized volatility in the SSECI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 740-749.
    11. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    12. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    13. Kulik, Rafal & Soulier, Philippe, 2011. "The tail empirical process for long memory stochastic volatility sequences," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 109-134, January.
    14. E. Barany & M. P. Beccar Varela & I. Florescu & I. Sengupta, 2012. "Detecting market crashes by analysing long-memory effects using high-frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 623-634, April.
    15. Cajueiro, Daniel O. & Tabak, Benjamin M., 2005. "The rescaled variance statistic and the determination of the Hurst exponent," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 172-179.
    16. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    17. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    18. Lim, Kian-Ping & Brooks, Robert D. & Kim, Jae H., 2008. "Financial crisis and stock market efficiency: Empirical evidence from Asian countries," International Review of Financial Analysis, Elsevier, vol. 17(3), pages 571-591, June.
    19. Mistrulli, Paolo Emilio, 2011. "Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1114-1127, May.
    20. Cannon, Michael J. & Percival, Donald B. & Caccia, David C. & Raymond, Gary M. & Bassingthwaighte, James B., 1997. "Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 606-626.
    21. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
    22. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    23. Andersen, J.V. & Sornette, D., 2004. "Fearless versus fearful speculative financial bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 565-585.
    24. Cajueiro, Daniel O & Tabak, Benjamin M, 2004. "The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 521-537.
    25. repec:cuf:journl:y:2013:v:14:i:3:kaminsky is not listed on IDEAS
    26. Al-Anaswah, Nael & Wilfling, Bernd, 2011. "Identification of speculative bubbles using state-space models with Markov-switching," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1073-1086, May.
    27. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.
    28. Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
    29. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    30. Mielniczuk, J. & Wojdyllo, P., 2007. "Estimation of Hurst exponent revisited," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4510-4525, May.
    31. Benoit Mandelbrot, 1965. "Forecasts of Future Prices, Unbiased Markets, and "Martingale" Models," The Journal of Business, University of Chicago Press, vol. 39, pages 242-242.
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    More about this item

    Keywords

    Fractional Brownian motion; Hurst coefficient; self-similarity; alpha-stable distributions; heavy tails; early warning indicator.;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • G01 - Financial Economics - - General - - - Financial Crises
    • G1 - Financial Economics - - General Financial Markets
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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