The efficient market hypothesis (EMH) fails as a valid model of financial markets. The fractal market hypothesis (FMH) is a more general alternative way to the EMH. The FMH is formed on the following parameter space: agents’ investment horizons. A financial market is more stable when a fractal character in the structures of agent’s investment horizons is adopted. For computer simulations, the c...

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put FMH into broader perspective, Random Walk and Efficient Hypotheses are considered together with basic principles fractal geometry. After exploring historical developments associated different hypotheses, an overview mathematical modelling is provided. The principal go...

A fractal approach is used to analyze financial time series, applying different degrees of time resolution, and the results are interrelated. Some fractal properties of foreign exchange (FX) data are found. In particular, the mean size of the absolute values of price changes follows a “fractal” scaling law (a power law) as a function of the analysis time interval ranging from a few minutes up t...

A new general model for asset returns is studied in the framework of the Fractal Market Hypothesis (FMH). To accomodate markets with arbitrage opportunities it concerns capital market systems in which the Conditionally Exponential Dependence (CED) property can be attached to each investor on the market. Emploing the limit theorem for the CED systems, the universal characteristics for the distri...

In this paper, we propose a new agent-based model to study the source of liquidity and the ‘‘emergent’’ phenomenon in financial market with fractal structure. Themodel rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stabi...

The chaos theory assumes that the returns dynamics are not normally distributed and more complex approaches have to be used to study these time series. In fact, the Fractal Market Hypothesis assumes that the returns dynamics are not independent of the investors’ attitudes and represent the result of the interaction of traders who, frequently, adopt different investment styles. The studies propo...