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 .
The level crossing and inverse statistics 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 6. We show that by using the level crossing analysis one can estimate how the DAX and oil time series will develop. We carry out same analysis for the increments of DAX and oil price log-returns ,(which is known as inverse statistics) and provide the distribution of waiting times to observe some level for the increments .
A
and inverse statistics
D
\approx
R
forecasts
estimate how
R
(normalized
will develop. We carry out same analysis for the increments of DAX and oil price
R
) with good precision for the levels in the interval -0.5 < \alpha < 0.5
,(which is known as inverse statistics) and provide the distribution of waiting times to observe some level for the increments