Complex Network Time Series Analysis of a Macroeconomic Model

Abstract

Time series produced by an idealized macro-economic model are analyzed by means of conversion to complex networks by three different methods: the recursive graph method, the natural visibility graph method and the ordinal partition graph method. For several values of one of the model’s control parameters yielding both fully chaotic time-series and intermittent chaos very close to periodicity the corresponding complex networks are obtained for each conversion algorithm, and several network metrics are evaluated: average degree, number of nodes, connectivity ratio, characteristic path length, clustering coefficient, assortativity and local dimensionality. Moreover, multifractal analysis of the chaotic time series is performed which reveals the multifractal structure of the orbits in phase space for the chaotic time series. This multifractal structure is also depicted in the scale-free nature of the corresponding complex networks which agrees with literature results. Most metrics clearly distinguish between fully chaotic and intermittent time series. Some metrics have significantly different values for chaotic series obtained at different values of the control parameter revealing subtle differences in phase space structure and system dynamics. The average degree of the ordinal partition networks together with assortativity showed that complex network time series analysis captures the repetition of particular patterns in the original time series and particular temporal correlations that would not be easy or even possible to capture with traditional non-linear analysis methods. Finally, the Lyapunov exponent of the time series is shown to be linearly correlated with the average local dimensionality metric of the complex network obtained by the visibility graph method, a result that is reported for the first time.