Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market
arXiv:cond-mat/0404416 · doi:10.1142/S0219024908005020
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.
16 pages, 11 figures. Added section on Variance Ratios, extended discussion with added reference
References in corpus (8)
- Detecting Long-range Correlations with Detrended Fluctuation Analysis
- Effect of Trends on Detrended Fluctuation Analysis
- A Random Matrix Approach to Cross-Correlations in Financial Data
- Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
- An analysis of Cross-correlations in South African Market data
- Quantifying dynamics of the financial correlations
- Identifying Business Sectors from Stock Price Fluctuations
- Identifying Complexity by Means of Matrices