Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis

Abstract

In this study, features of the financial returns of the PSI20index, related to market efficiency, are captured using wavelet-and entropy-based techniques. This characterization includes the following points. First, the detection of long memory, associated with low frequencies, and a global measure of the time series: the Hurst exponent estimated by several methods, including wavelets. Second, the degree of roughness, or regularity variation, associated with the Hölder exponent, fractal dimension and estimation based on the multifractal spectrum. Finally, the degree of the unpredictability of the series, estimated by approximate entropy. These aspects may also be studied through the concepts of non-extensive entropy and distribution using, for instance, the Tsallis q-triplet. They allow one to study the existence of efficiency in the financial market. On the other hand, the study of local roughness is performed by considering wavelet leader-based entropy. In fact, the wavelet coefficients are computed from a multiresolution analysis, and the wavelet leaders are defined by the local suprema of these coefficients, near the point that we are considering. The resulting entropy is more accurate in that detection than the Hölder exponent. These procedures enhance the capacity to identify the occurrence of financial crashes.

A Vibration Analysis Based on Wavelet Entropy Method of a Scroll Compressor

“…It combines wavelet decomposition and entropy to estimate the degree of disorder of a signal with a high time-frequency resolution. Recently, WE has been used in engineering signal surveys such as electroencephalography (EEG) testing, climate processes, machinery vibration detection, and fault diagnosis and so on [18][19][20][21][22]. The results of these studies have manifested its better performance in analyzing the variability and complexity of signals compared with traditional methods.…”

Wavelet Leader and Multifractal Detrended Fluctuation Analysis of Market Efficiency: Evidence from the WAEMU Market Index

“…Many previous studies make use of the Hurst exponent in the analyses of weak form market efficiency (Pascoal & Monteiro, 2014;Kumar & Kamaiah, 2014). Wang et al (2009) using MF-DFA divides their series into sub-series and finds that Shenzhen stock market was becoming more and more efficient by analysing the change of Hurst exponent and a new practical measure, which is equal to multifractality degree sometimes.…”

Long Memory and Fractality Among Global Equity Markets: a Multivariate Wavelet Approach

“…Boubaker and Peguin-Feissolle (2013) proposed semiparametric wavelet base long memory estimators and demonstrated its superiority, with respect to several non-wavelet estimators, using simulation experiments. More recently,Pascoal and Monteiro (2014), investigating the predictability of the Portuguese stock returns using wavelet estimators of long memory, fractal dimension and the Holder exponent, found no evidence of long memory in the PSI20 returns, thereby confirming the efficiency of the Portuguese equity market. This paper investigates long memory among global equity markets using estimators from the wavelet domain.…”