Possible Statistical Comparison of Two Time Series

The most often discussed problem is the comparison of two time series (for example financial or non-financial time series). The proposed approach can be assessed on the base of knowledge of the set of past values and the assumption that there is no significant change in the used probability model. The presented paper is motivated by the approach of positive and quadrant dependence. There is a "power of matching" between two time series, which can be measured (or estimated) in many ways. The problem may occur with their non-stationarity. One solution to this problem can be the quantification of preserving (or not preserving) probability of a monotone relationship. It means the probability that the values of the first time series are increasing and the values of the second time series are also increasing and similarly for consistent decreases. One measure for this quantification is proposed here followed by application on real data sets (Prague Stock Exchange) to estimate the price of one asset depending on the price of another asset.