Noise estimation by use of neighboring distances in Takens space and its applications to stock market data

We present a method that uses distances between nearest neighbors in Takens space to evaluate a level of noise. The method is valid even for high noise levels. The method has been verified by estimation of noise levels in several chaotic systems. We have analyzed the noise level for Dow Jones and DAX indexes and we have found that the noise level ranges from 25 to 80 percent of the signal variance.