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

Avishek Bhandari,Bandi Kamaiah

doi:10.1007/s40953-020-00220-0

Avishek Bhandari, Bandi Kamaiah

Open Access

https://doi.org/10.1007/s40953-020-00220-0

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Abstract

This paper seeks to understand the long memory behaviour of global equity returns using novel methods from wavelet analysis. We implement the wavelet based multivariate long memory approach, which possibly is the first application of wavelet based multivariate long memory technique in finance and economics. In doing so, long-run correlation structures among global equity returns are captured within the framework of wavelet-multivariate long memory methods, enabling one to analyze the long-run correlation among several markets exhibiting both similar and dissimilar fractal structures.

Highlights

The estimation and the analysis of long memory parameters have mainly focused on the analysis of long-range dependence in stock return volatility using traditional time and spectral domain estimators of long memory
The empirical analysis first proceeds with visually analyzing the dynamic nature of long memory of select equity returns, as given by the time-series plot of long memory estimates, which is obtained by applying the wavelet based estimator of the Hurst exponent developed by Abry and Veitch (1998) and Abry et al (2003) in a rolling windows framework
This paper investigated the phenomenon of long memory among global equity returns using methods from both univariate and multivariate class of wavelet based long memory estimators

Summary

Introduction

The estimation and the analysis of long memory parameters have mainly focused on the analysis of long-range dependence in stock return volatility using traditional time and spectral domain estimators of long memory. The definitive ubiquity and existence of long memory in the volatility, estimated or generated using various methods, of stock returns is an established stylized fact. The presence of long memory requires major revisions in the standard estimation procedures without which the estimated results can be seriously biased. In this paper on long memory among global equity markets, several wavelet based estimators are applied to test for the presence of long memory in the global equity returns and returns volatility. The presence of long memory in the volatility of the stock returns as well as some returns themselves is demonstrated from the empirical evidences. Phases of efficiency and inefficiency of markets, as adjudicated by presence of both long memory and no-memory, is evidenced when the analysis is performed using rolling windows.

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