Fractal structure of financial high frequency data

We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values. Using these extreme values determined by a scale, we define some functions. Moreover, using these functions, we can measure a kind of fractal dimension - fold dimension. In financial high frequency data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly sampling. Further, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.