Complex systems are characterized by deterministic laws (which often may be hidden) and randomness. A tool to analyse those systems is recurrence quantification analysis (RQA). RQA does not rely on any sort of assumption of stationarity and is not sensitive to singularities and transitions. It...

R.G. Goodwin mentioned that "economists will be led, as natural scientists have been led, to seek in nonlinearities an explanation of the maintenance of oscillation" (Goodwin, Econometrica 19(1), 1951); following this reasoning, we studied business cycles as if they were generated by nonlinear...

This chapter is dedicated to describe RQA applications in detecting spatio-temporal recurrent patterns of dynamical regimes of economic time series. Here we investigate the nature of economic dynamics and specifically of business cycles Orlando and Zimatore (Chaos, Solitons Fractals 110:82–94,...

This paper proposes a novel and simple approach to compute daily Value at Risk (VaR) and Expected Shortfall (ES) directly from high-frequency data. It assumes that financial logarithm prices are subordinated unifractal processes in the intrinsic time, which stochastically transforms the clock...

In this Chapter, we provide the definitions, notions and examples relevant for the analysis of the dynamical systems of interest to us in the remainder of this book. We start with with a description of dynamical systems and we provide a taxonomy. Then, we define continuous-time dynamical systems...

In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of...