SERIAL CORRELATION, PERIODICITY AND SCALING OF EIGENMODES IN AN EMERGING MARKET

Diane Wilcox () and Tim Gebbie ()
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Diane Wilcox: School of Computational & Applied Mathematics, University of Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa
Tim Gebbie: School of Computational & Applied Mathematics, University of Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa;

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 07, 739-760

Abstract: We investigate serial correlation, periodic, aperiodic and scaling behavior 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 behavior 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.

Keywords: Emerging markets; random matrices; random walk hypothesis; long memory (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024908005020

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