Autoregressive models as a tool to discriminate chaos from randomness in geoelectrical time series: an application to earthquake prediction

Abstract

The time dynamics of geoelectrical precursory time series has been investigated and a method to discriminate chaotic behaviour in geoelectrical precursory time series is proposed. It allows us to detect low-dimensional chaos when the only information about the time series comes from the time series themselves. The short-term predictability of these time series is evaluated using two possible forecasting approaches: global autoregressive approximation and local autoregressive approximation. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a test to discriminate between low-dimensional chaos and random dynamics. The analyzed time series are geoelectrical measurements recorded by an automatic station located in Tito (Southern Italy) in one of the most seismic areas of the Mediterranean region. Our findings are that the global (linear) approach is superior to the local one and the physical system governing the phenomena of electrical nature is characterized by a large number of degrees of freedom. Power spectra of the filtered time series follow a P(f) = F-a scaling law: they exhibit the typical behaviour of a broad class of fractal stochastic processes and they are a signature of the self-organized systems.