Analysis of the Romanian Capital Market Using the Fractal Dimension

Abstract

The surrounding reality can be analyzed due to the interaction of complex nonlinear dynamic systems. The article’s main objective is to develop and analyze the models that best describe the efficient behavior of the Romanian capital market that generated the analyzed time series. The empirical analysis carried out in this paper does not aim to classify the Romanian market capital as efficient or ineffective but rather to identify the degree of deviation from efficiency relative to other markets, namely, an analysis of the dynamics of the degree of deviation over time. To describe the distribution of returns, we focused on the family of generalized hyperbolic distributions, which have statistical properties similar to financial returns. The presence of wide tails in the distributions (of extreme values) suggests using statistical tests and measures to detect dependencies, which take this behavior into account. Statistical methods and efficiency indicators are used, such as the Hurst exponent, Taken’s theorem, and the fractal dimension, which facilitate the detection of the main types of dependencies that could be present in the return series; measures that are robust to the heteroscedastic behavior of the returns. These statistical measures are applied to the entire period and sliding windows.

Keywords

• information efficiency
• long-term memory
• fractal dimension
• Hurst exponent
• chaos theory
• short-term memory