Markov property of the extremes in the binned random walk time series

Random walk is an important reference process in statistics and its properties have to be studied in financial applications, where hypothetic random walk of price remains an essential component of efficient market theories. Our day and hour time-scale predictive models demonstrated stable positive correlations between reality and prediction for returns taken in the time series of the respective (daily and hourly) lows and highs. However, same property is shown to hold for the simple Brownian motion random walk model. What are the origins and the implications of this effect?

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