Physics of Risk

One of the conclusions of fractal geometry is a fact that fractals unlike traditional Euclidean shapes lack characteristic scale. Those “fractured” objects are self-similar – defining geometry is clearly visible on multitude of scales. It is known that self-similarity is observed not only in formally defined geometric objects, such as Sierpinsky triangle or Koch snowflake, but also in the surrounding nature. One of my most favorite examples is a comparison of tree, its branches and a leaf (for more inspiring examples see introduction of Fractals section) – they all have branching structure and something green filling the extra space in between.

The interesting thing, in context of the topic in focus, is that one can extend fractal formalism beyond formal or natural geometric shapes. It is also noticed that some of the natural processes exhibit fractal features in their time series! It is known that geoelectrical processes 1, heartbeat 2 and even human gait 3 time series posses this feature. While financial market, frequently analyzed on Physics of Risk website, time series are also no exception 4, 5. Though the aforementioned time series are much more complex – they exhibit not monofractality (single manner self-similar behavior as the aforementioned formal geometric fractals do), but multifractality! Continue reading “Multifractality of time series” »