Discriminating randomness from chaos with application to a weather time series

A new method is presented which permits one to discriminate low-dimensional chaos from randomness. The method consists in fitting autoregressive processes to the data and forecasting future values of the system on the basis of the model selected. We distinguish between 2 possible forecasting techniques of a dynamical system given by experimental series of observations. The “global autoregressive approximation” views the observations as a realization of a stochastic process, whereas the “local autoregressive approximation” views the observations as the realizations of a truly deterministic process. A proper comparison between the predictive skills of the 2 techniques allows us to gain insight into distinguishing low-dimensional chaos from randomness. The procedure has been applied to a daily temperature time series recorded in Trieste (Italy) over the past 40 years (1950—1989). The analysis gives no evidence for low-dimensional chaos, the dynamics being compatible with a limit cycle blurred by red noise.