The level crossing analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, \alpha^+, where T_{\alpha} =1/\alpha^+ is the average waiting time for observing the level \alpha again. We estimate the probability P(K, \alpha), which provides us the probability of observing K times of the level \alpha with positive slope, in time scale T_{\alpha}. For analyzed time series we found that maximum K is about \approx 6. We show that by using the level crossing analysis one can forecasts the DAX and oil time series (normalized log-returns) with good precision for the levels in the interval -0.1 < \alpha < 0.1 and -0.35 < \alpha < 0.35, respectively .
The level crossing analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, \alpha^+, where T_{\alpha} =1/\alpha^+ is the average waiting time for observing the level \alpha again. We estimate the probability P(K, \alpha), which provides us the probability of observing K times of the level \alpha with positive slope, in time scale T_{\alpha}. For analyzed time series we found that maximum K is about \approx 6. We show that by using the level crossing analysis one can forecasts the DAX and oil time series (normalized log-returns) with good precision for the levels in the interval -0.5 < \alpha < 0.5 .
R
-0.1
-0.5
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0.1 and -0.35 < \alpha < 0.35, respectively
0.5