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We consider a Green's function solution to the Classical Kolmogorov- Feller Equation which requires an iterative approach for which a sufficient convergence condition is derived. The solution obtained is applied to the simulation of signals whose spectral properties are determined by a Characteristic Function of the form j k jq; q > 0 where k is the spatial frequency and q is the 'Fourier Dimension'. Using example macroeconomic financial time series (FTSE Close-of-Day and the Dow Jones Industrial Average), correlations are observed to exist between q and long term trends in the series using a standard moving window process. This result provides the potential for developing an accurate short term forecasting strategy.
Blackledge, Jonathan; Lamphiere, Marc; Murphy, Kieran; Overton, Shaun; and Panahi, Afshin, "Simulation and Analysis of Stochastic Signals using the Kolmogorov-Feller Equation" (2012). Articles. Paper 48.