The Surface Division Method as variability measure of discrete and continuous time series

Abstract

One of the most important issues to be decided in the analysis of time series is to determine their variability and to identify the process of shaping their values. In the classical approach, volatility is most often identified with the variance of growth rates. Meanwhile, the nature of risk is not only the variability, but also the predictability of changes, which can be assessed using the fractal dimension. The aim of the article is to present the application of the fractal dimension estimated by the surface division method to evaluate the variability of time series. The paper presents the method of determining the fractal dimension, its interpretation, the significance table and the application example. Specific cases show differences between the use of standard deviation and the fractal dimension for risk assessment. The fractal dimension appears here as a method to assess the degree of stability of variations. This article is an extension of the previously presented method for discrete time series to continuous time series.