Fractal Markets, Fractional Integration, and Long Memory in Financial Time Series – I

The concepts – ‘fractal market hypothesis,’ ‘fractional integration of time series,’ and ‘long memory and persistence in time series’ – are related in terms of their proponents and history.

I’m going to put up ideas, videos, observations, and analysis relating to these concepts over the next several posts, since, more and more, I think they lead to really fundamental things, which, possibly, have not yet been fully explicated.

And there are all sorts of clear connections with practical business and financial forecasting – for example, if macroeconomic or financial time series have “long memory,” why isn’t this characteristic being exploited in applied forecasting contexts?

And, since it is Friday, here are a couple of relevant videos to start the ball rolling.

Benoit Mandelbrot, maverick mathematician and discoverer of ‘fractals,’ stands at the crossroads in the 1970’s, contributing or suggesting many of the concepts still being intensively researched.

In economics, business, and finance, the self-similarity at all scales idea is trimmed in various ways, since none of the relevant time series are infinitely divisible.

A lot of energy has gone into following Mandelbrot suggestions on the estimation of Hurst exponents for stock market returns.

This YouTube by a Parallax Financial in Redmond, WA gives you a good flavor of how Hurst exponents are being used in technical analysis. Later, I will put up materials on the econometrics involved.

Blog posts are a really good way to get into this material, by the way. There is a kind of formalism – such as all the stuff in time series about backward shift operators and conventional Box-Jenkins – which is necessary to get into the discussion. And the analytics are by no means standardized yet.

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