Application of the fractal market hypothesis for macroeconomic time series analysis

Abstract — This paper explores the conceptual background to financial time series analysis and financial signal processing in terms of the Efficient Market Hypothesis. By revisiting the principal conventional approaches to market analysis and the reasoning associated with them, we develop a Fractal Market Hypothesis that is based on the application of non-stationary fractional dynamics using an operator of the type ∂2 ∂x2 − σq(t) ∂ q(t) ∂tq(t) where σ−1 is the fractional diffusivity and q is the Fourier dimension which, for the topology considered, (i.e. the one-dimensional case) is related to the Fractal Dimension 1 < DF <