Generalized Auto-Correlation and its Application in Deterministic Chaos of Continuous Non-Stationary Time Series

Abstract

The paper first modifies the notion of auto-correlation between two stages of a signal, so that it is applicable to any time series,
stationary/ non-stationary. Next it generalizes the notion further to compare three stages of the time series simultaneously. The comparison is based on two even / uneven time-delays with two/ three dimensional correlogram diagrams. As a result three stages of the time series may be simultaneously tested to be independent. As an application, continuous non-stationary signals like ECG and music signals are investigated for the existence of deterministic chaos in two and three dimensions.