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The Hurst exponent is the only real number required to describe a type of stochastic process known as fractal Brownian motion that is employed to model time series of financial origin. The Hurst exponent can also be taken as a measure of the long term memory of time series. In this work we analyze four daily time series of prices (Open, Close, High and Low) of some American and European stock indices. There are very few studies of the characteristics of daily High and Low time series. However, an empirical, in-depth, comparative study of all four series reveals some consistent patterns at the day-to-day time scale. In all the cases considered, the Hurst exponents of High and Low time series are appreciably higher than those obtained for Open and Close. Our analysis indicates that High and Low index values are more persistent (positively auto-correlated) and, therefore, more predictable than Open and Close values, whose time series fluctuate between persistence and anti-persistence (negative auto-correlation) and in the long term have a Hurst exponent close to 0.5, characteristic of a random walk process.
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