Unifractality and Multifractality in the Italian Stock Market

Abstract

Tests for random walk behaviour in the Italian stock market are presented, based on an investigation of the fractal properties of the log returns series for the Mibtel index. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Critical values for the test statistics are generated using Monte Carlo simulations of random Gaussian innovations. Evidence is reported of multifractality, and the departure from random walk behaviour is statistically significant on standard criteria. The observed pattern is attributed primarily to fat tails in the returns probability distribution, associated with volatility clustering in returns measured over various time scales.

Keywords: random walk, unifractality, multifractality, Italy, stock market

JEL Classification: G1, F3