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This paper considers the Fractal Market Hypothesis (FMH) for assessing the risk(s) in developing a financial portfolio based on data that is available through the Internet from an increasing number of sources. Most financial risk management systems are still based on the Efficient Market Hypothesis which often fails due to the inaccuracies of the statistical models that underpin the hypothesis, in particular, that financial data are based on stationary Gaussian processes. The FMH considered in this paper assumes that financial data are non-stationary and statistically self-affine so that a risk analysis can, in principal, be applied at any time scale provided there is sufficient data to make the output of a FMH analysis statistically significant. This paper considers a numerical method and an algorithm for accurately computing a parameter - the Fourier dimension - that serves in the assessment of a financial forecast and is applied to data taken from the Dow Jones and FTSE financial indices. A more detailed case study is then presented based on a FMH analysis of Sub-Prime Credit Default Swap Market ABX Indices.
Blackledge, J.: Systemic Risk Assessment using a Non-stationary Fractional Dynamic Stochastic Model for the Analysis of Economic Signals. ISAST Transactions on Computers and Intelligent Systems, vol: 2, issue: 1, pages: 76 - 94, 2010.