ABSTRACT
The basic objective of time series analysis is to understand the characteristics of the processes that generate the time series of data and to make future predictions and simulations under different scenarios. Reconstruction of the phase space from a univariate time series is carried out using the embedding theorem, and the important invariant measures such as the Lyapunov exponent, KS entropy, and correlation dimension, which give useful information for diagnosing, modelling, and predicting the system, are computed in this space. Therefore, it is necessary to look for alternative methods of modelling and forecasting. The procedure for modelling a chaotic time series starts with embedding the data in a phase space. When a non-linearity test is performed, it is desirable to choose a test statistic that is useful for non-linear deterministic modelling, although a positive test for non-linearity does not guarantee the same result for determinism.
