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A class of micropulses and antipersistent fractional Brownian motion

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Author Info

  • Cioczek-Georges, R.
  • Mandelbrot, B. B.

Abstract

We begin with stochastic processes obtained as sums of "up-and-down" pulses with random moments of birth [tau] and random lifetime w determined by a Poisson random measure. When the pulse amplitude [var epsilon] --> 0, while the pulse density [delta] increases to infinity, one obtains a process of "fractal sum of micropulses." A CLT style argument shows convergence in the sense of finite dimensional distributions to a Gaussian process with negatively correlated increments. In the most interesting case the limit is fractional Brownian motion (FBM), a self-affine process with the scaling constant . The construction is extended to the multidimensional FBM field as well as to micropulses of more complicated shape.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 60 (1995)
Issue (Month): 1 (November)
Pages: 1-18

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Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:1-18

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Related research

Keywords: Fractal sums of pulses Fractal sums of micropulses Fractional Brownian motion Poisson random measure Self-similarity Self-affinity Stationarity of increments;

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Citations

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Cited by:
  1. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series 2046, CESifo Group Munich.
  2. Dominique Guegan, 2005. "How can we Define the Concept of Long Memory? An Econometric Survey," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 113-149.
  3. Rea, William & Oxley, Les & Reale, Marco & Brown, Jennifer, 2013. "Not all estimators are born equal: The empirical properties of some estimators of long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 29-42.
  4. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
  5. Guglielmo Maria Caporale & Luis Gil-Alana, 2004. "Long range dependence in daily stock returns," Applied Financial Economics, Taylor & Francis Journals, vol. 14(6), pages 375-383.
  6. Francis Ahking, 2010. "Non-parametric tests of real exchange rates in the post-Bretton Woods era," Empirical Economics, Springer, vol. 39(2), pages 439-456, October.
  7. Luis Gil-Alana, 2003. "Stochastic behavior of nominal exchange rates," Atlantic Economic Journal, International Atlantic Economic Society, vol. 31(2), pages 159-173, June.
  8. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
  9. Cioczek-Georges, R. & Mandelbrot, B. B., 1996. "Alternative micropulses and fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 143-152, November.
  10. Fischer, Christian & Gil-Alana, Luis A., 2006. "The nature of the relationship between international tourism and international trade: the case of German imports of Spanish wine," 98th Seminar, June 29-July 2, 2006, Chania, Crete, Greece 10049, European Association of Agricultural Economists.
  11. L. A. Gil-Alana, 2003. "A fractional integration analysis of the population in some OECD countries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1147-1159.
  12. Luis Gil-Alana, 2004. "The dynamics of the real exchange rates in Europe: a comparative study across countries using fractional integration," Applied Economics Letters, Taylor & Francis Journals, vol. 11(7), pages 429-432.

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