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

TL;DR

This paper introduces a noise estimation method based on neighboring distances in Takens space, effective even at high noise levels, and applies it to analyze stock market data, revealing significant noise proportions.

Contribution

The paper proposes a novel noise estimation technique using Takens space neighbor distances, validated on chaotic systems and applied to stock market indices.

Findings

Noise levels in Dow Jones and DAX range from 25% to 80% of signal variance.

Method remains effective at high noise levels.

Stock market data contains substantial noise.

Abstract

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.