Fractals and Intrinsic Time – a Challenge to Econometricians

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 to a year. In an autocorrelation study of intra-day data, the absolute values of price changes are seen to behave like the fractional noise of Mandelbrot and Van Ness rather than those of a GARCH process. Intra-day FX data exhibit strong seasonal and autoregressive heteroskedasticity. This can be modeled with the help of new time scales, one of which is termed intrinsic time. These time scales are successfully applied to a forecasting model with a “fractal” structure for FX as well as interbank interest rates, the latter presenting market structures similar to the Foreign Exchange. The goal of this paper is to demonstrate how the analysis of high-frequency data and the finding of fractal properties lead to the hypothesis of a heterogeneous market where different market participants analyze past events and news with different time horizons. This hypothesis is further supported by the success of trading models with different dealing frequencies and risk profiles. Intrinsic time is proposed for modeling the frame of reference of each component of a heterogeneous market.