Volatility of fractal and multifractal time series

Many systems in nature generate time series with complex behavior often associated with the so-called scaling laws. Examples from geophysical science include time series of temperature, precipitation, earthquakes, and floods. Studying such time series may help to reveal the mechanism that generates them. In this paper we show how complex long-range correlations in time records (whose values approximately follow a Gaussian distribution) may be identified by a simple method - the volatility test. We explain the relation between high-order correlations and self-affine (fractal and multifractal) behavior, and show how the existence of volatility correlations can give a simple indication for multifractality. We demonstrate our method on daily deep ocean temperature records from the equatorial Pacific - the region of the El-Nino phenomenon.