The multiscale large deviation spectrum based on higher moments for financial time series

Abstract

In this letter, based on large deviations theory, we propose to use higher moments (e.g., skewness, kurtosis) to investigate the multifractal features of large deviations spectrum. It is different from the estimation of the spectrum using another roughness exponent, such as oscillation-based grain exponent. When using statistical skewness and kurtosis as roughness exponent, the traditional normalization procedure of signals fails. To overcome this problem, a new approach is proposed. The large deviations spectrum on both artificial and financial time series is estimated. Comparing with another multifractal analysis, we verify that large deviations spectrum overcomes the limitations of Legendre spectrum, and the proposed method is able to reveal significant information that remains hidden with Legendre spectrum. The properties of scaling behavior using a modified scaling/non-scaling criterion are discussed. Meanwhile, we study the scaling behavior of time series and quantify the presence or absence of scale invariance of financial signals.