Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market

TL;DR

This study analyzes eigenmodes of correlation matrices from South African stock data, revealing calendar effects, serial correlation, and long-term memory in eigenmodes, with implications for data handling and market understanding.

Contribution

It is the first to examine eigenmodes' periodicity, serial correlation, and scaling in an emerging market, highlighting the impact of data interpolation on spectral properties.

Findings

Calendar effects limited to eigenmodes outside Wishart range

Serial correlation detected in first eigenmodes

Long-term memory effects present in top eigenmodes

Abstract

We investigate serial correlation, periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. Periodic, or calendar, components are detected by spectral analysis. We find that calendar effects are limited to eigenmodes which correspond to eigenvalues outside the Wishart range. Using a variance ratio test, we uncover serial correlation in the first eigenmodes and find slight negative serial correlation for eigenmodes within the Wishart range. Our spectral analysis and variance ratio investigations suggest that interpolating missing data or illiquid trading days with zero-order hold introduces high frequency noise and spurious serial correlation. Aperiodic and scaling behaviour of the eigenmodes are investigated by using rescaled-range (R/S) methods and detrended fluctuation analysis (DFA). We find that DFA and classic and modified R/S exponents suggest the presence of long-term memory effects in the first five eigenmodes.