Limitations of efficiency and of martingale models

  • Benoit B. Mandelbrot


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 \(\Lambda = \sum\nolimits_{m = 0}^\infty {L(m)} \).


Spectral Density Price Change Infinite Horizon Finite Variance Price Series 
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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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