Diagnosing time series dynamical structures

A sequence of two tests is proposed to diagnose time series dynamical structures. The first is known as the BDS test. It determines whether a series that is free from linear structure is independently and identically distributed noise (iid). If the series is not iid, a β test (proposed in this paper) associates the structure with the seriesʹ signal to noise ratio. Based upon observed phenomena and empirical evidence, the test is found to be capable of distinguishing between nonlinear stochastic processes with signal to noise ratio less than four and strictly deterministic processes with low attractor dimension. It may confuse high signal to noise ratio nonlinear stochastic processes with more complex deterministic processes that have high attractor dimension and low ratio.