Fractal Market Hypothesis, Trend Analysis and Future Price Prediction

Dear Colleagues,

In 1900, Louis Bachelier concluded that the price of a commodity today is the best estimate of its price tomorrow–‘there is no useful information contained in historical price movements of securities’. The random behaviour of commodity prices was again noted by the economist Holbrook Working in 1934 in an analysis of financial time series data. In the 1950s, Maurice Kendall attempted to find periodic cycles in the financial time series of various securities and commodities but did not observe any. Prices appeared to be yesterday’s price plus some random change (up or down) and he suggested that price changes were independent and followed random walks. Thus, the first models conceived for price variation were based on the sum of independent random variations often referred to as Brownian motion. This led to the Random Walk Hypothesis and the closely associated Efficient Market Hypothesis which states that random price movements indicate a well-functioning or efficient market, a concept which emerged in the mid-1960s. This hypothesis assumes that there is a rational and unique way to use available information, that all agents possess this knowledge and that any chain reaction produced by a ‘shock’ happens instantaneously. This is clearly not physically possible and financial models that are based on such a hypothesis have and will continue to fail.

The Fractal Market Hypothesis emerged in the 1990s with the work of Edgar Peters (an asset manager) and Benoit Mandelbrot (a mathematician), for example. This was a natural consequence of the work of the latter mathematician and others to develop the subject of fractal geometry, an icon of which is Mandelbrot’s famous book The Fractal Geometry of Nature first published in 1982. The hypothesis states that financial time series exhibit self-affine structures. Price variations are in effect random walks whose statistical distribution of values is similar over different time scales. Ralph Elliott (a professional accountant) first reported on the apparent self-affine properties of financial data in 1938. He was the first to observe that segments of financial time series data of different sizes could be scaled in such a way that they were statistically the same, producing so called ‘Elliot Waves’. The Elliott wave principal developed in the late 1930’s and the Fractal Market Hypothesis developed in the late 1990’s provides data consistent models for the interpretation and analysis of financial signals and investment theory. The key to this is that fractal time series have an inherent memory and thus, the price of a commodity tomorrow is determined in some way by the characteristics of the past.  The importance of this observation in financial analysis is self-evident and has been the subject of research over the past few decades. This has, more recently, included the connectivity between memory, self-affinity and Fractional Calculus when the fractional derivative of a function depends on the ‘history’ of that function. One of the reasons that financial time series and other financial data have emerged to have self-affine properties is due to the innate complexity of the world economic system. This includes the (in)stabilities that have become evident in more recent times. The dynamics of market prices have become a reflection of the multitude of interactions between agents with different investment horizons and different views on the interpretation of information leading to disruptions and to crashes when these interactions are broken.

For this Special Issue, the focus is on the applications of the Fractal Market Hypothesis to trend analysis and future price prediction. Submissions are encouraged from researchers and practitioners to illustrate the value (or otherwise) that this hypothesis has in predicting the future behaviour of the markets in both the long and short term.  In additional to articles on the development and applications of algo-trading based on the Fractal Market Hypothesis, for example, this Special Issue is also interested in articles that provide a broader perspective on the influence that the hypothesis has had in a global economic context. 

Prof. Dr. Jonathan Blackledge
Guest Editor

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