Detection of Nonlinearity and Stochastic Nature in Time Series by Delay Vector Variance Method

This paper investigates the suitability of Delay Vector Variance (DVV) algorithm in determining the presence of non-linear and stochastic nature of time series both in the presence and absence of chaos. A differential entropy based method is used to find the optimum embedding dimension and time lag which are needed to represent the time series in phase space. Results obtained from the simulation indicate that the DVV method gives quantitative and easy to interpret output to characterize the underlying times series in terms of non-linear and stochastic nature. I. INTRODUCTION Atime series becomes chaotic due to the presence of determinism, non-linearity and strange attractor in it. So chaos implies non-linearity but not vice-versa. Since many non-linearity analysis techniques rest upon chaos theory, the properties such as determinism and presence of strange attractor have often been confounded with the no n-linear behavior. So the presence of strange attractor would lead to the conclusion that the time series is non-linear while it is not necessarily so. As a result determinism and non-linearity have been confounded in time series signal analysis. Methods introduced by Kaplan[1] and by Kennel et al.[2] both rest upon the examination of the predictability of a time series. Furthermore, Kaplan " s " δ-ε " method has been used in combination with the surrogate data [3] strategy for examining the linear or non-linear nature of time series. Kaplan " s method has short comings. It's main shortcoming is in the large spread of results for surrogate data which tends to decrease the significance of results found with delta-epsilon. There is also Surrogate method [4] of testing non-linearity but there is a chance of false rejection of the null hypothesis due to stringent definition of linearity of the time series itself. Another classic method to detect non-linearity is " Deterministic versus Stochastic " (DVS) [5] plots. But DVS method does not allow for a quantitative analysis. Another approach to non-linearity detection is Correlation Exponents