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Markov analysis and kramers-moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price

Ghasemi, F ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.75.060102
  3. Publisher: 2007
  4. Abstract:
  5. We describe a general method for analyzing a nonstationary stochastic process X (t) which, unlike many of the previous analysis methods, does not require X (t) to have any scaling feature. The method is used to study the fluctuations in the daily price of oil. It is shown that the returns time series, y (t) =ln [X (t+1) X (t)], is a stationary and Markov process, characterized by a Markov time scale tM. The coefficients of the Kramers-Moyal expansion for the probability density function P (y,t y0, t0) are computed. P (y,t, y0, t0) satisfies a Fokker-Planck equation, which is equivalent to a Langevin equation for y (t) that provides quantitative predictions for the oil price over times that are of the order of tM. Also studied is the average frequency of positive-slope crossings, να+ =P (yi >α, yi-1 <α), for the returns, where T (α) =1 να+ is the average waiting time for observing y (t) =α again. © 2007 The American Physical Society
  6. Keywords:
  7. Economic analysis ; Nonlinear equations ; Petroleum industry ; Probability density function ; Time domain analysis ; Fokker-Planck equation ; Kramers-Moyal expansion ; Markov analysis ; Nonstationary stochastic processes ; Markov processes
  8. Source: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 75, Issue 6 , 2007 ; 15393755 (ISSN)
  9. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.75.060102