Abstract
We propose a new method to describe fractal structure of data, which are non-equidistant in physical time, and apply this method to fractional Brownian motions. Using extended extreme values, we define functions independent of time scale. Moreover, a kind of fractal dimension is measured. In high frequency financial data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly resampling. Moreover, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor with constant transaction costs.
