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We study here the behaviour of the first three eigenvalues (λ 1 , λ 2 , λ 3 ) and their ratio [(λ 1 /λ 2 ), (λ 1 /λ 3 ), (λ 2 /λ 3 )] of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets. It has been known for some time that the largest eigenvalue (λ 1 ) contains information on the risk associated with the particular assets of which the covariance matrix is comprised. Here, we wish to ascertain whether the subdominant eigenvalues (λ 2 , λ 3 ) hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets. To do this, we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component. Our results appear to indicate that mature markets respond to crashes differently to emerging ones, in that emerging markets may take up to two months to recover while major markets take less than a month to do so. In addition, the results appears to show that the subdominant eigenvalues (λ 2 , λ 3 ) give additional information on market movement, especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics.

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Donner et al components, and (iii) low-frequency variability indicating a true longrange dependent process. In the presence of such multi-scale variability, common estimators of long-range memory in time series are prone to fail if applied to the raw data without previous separation of timescales with qualitatively different dynamics.

The purpose of paper is to assess the long-term memory of stock index returns in the pan-European platform Euronext AEX,. We find evidence of time dependency in much of the data, suggesting that the series may best be described as fractional Brownian motion. Modified Rescaled-Range Analysis and Detrended Fluctuation Analysis were used to measure the degree of long memory. The global Hurst exponents evidence persistent long memory in the Dutch, Belgian and Portuguese markets. In the French market, evidence of long memory is inconsistent and weak. Fractal structure suggests non-conformity with the Efficient Market Hypothesis, and may compromise the reliability of asset pricing models. Furthermore, time-dependent Hurst exponents show evidence of weakening persistence in these markets, particularly after the international crises of 2000, 2002 and 2010. A possible explanation for those changes is that the markets may have matured over time, becoming more efficient after these severe events.