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Limitations of efficiency and of martingale models

  • Benoit B. Mandelbrot
Chapter

Abstract

In the moving away process
$$C(t) = \sum\limits_{s = - \infty }^t {L(t - s)N(s)} $$
, the quantities N(s), called “innovations,” are random variables with finite variance and are orthogonal (uncorrelated) but are not necessarily Gaussian. Knowing the value of C(s) for s < t, that is, knowing the present and past “innovations” N(s),the optimal least squares estimator of C(t + n) is the conditional expected value E c C(t + n) In terms of the N(s),
$${E_c}C(t + n) = \sum\limits_{s = - \infty }^t {L(t + n - s)N(s)} $$
, which is a linear function of the N(s) for st. This paper that the large n behavior of E c C(t + n) depends drastically on the value of \(\Lambda = \sum\nolimits_{m = 0}^\infty {L(m)} \).

Keywords

Spectral Density Price Change Infinite Horizon Finite Variance Price Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Benoit B. Mandelbrot
    • 1
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA

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