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To explore the multivariable financial time series, first of all, the concepts related to financial time series are introduced. The phase space reconstruction theory is described firstly and then the methods for testing the nonlinear characteristics of financial time series are expounded, namely Hurst index and BDS testing. Secondly, the phase space reconstruction and nonlinear test of multivariable financial time series are discussed. Several sets of composite index and industry index of Shanghai security market in China are selected as the objects for the analysis of multivariable financial time series. The multivariable reconstruction methods are used to study the system reconstruction issue. Finally, the computation of nonlinear invariants in multivariate financial time series is explored by using the maximum Lyapunov exponent. The research results show that the maximum Lyapunov exponent and correlation dimension calculated by multivariate reconstruction are significantly higher than those calculated by univariate environment, showing stronger nonlinear characteristics. It can be seen that it is effective and feasible to reconstruct phase space using multivariate financial data and predict it by using nonlinear time series method.

Exploration of Multivariable Financial Time Series based on Algorithm