The autodependogram: a graphical device to investigate serial dependences

In this article the serial dependences between the observed time series and the lagged series, taken into account one-by-one, are graphically analysed by what we have chosen to call the “autodependogram”. This tool is a sort of natural nonlinear counterpart of the well-known autocorrelogram used in the linear context. The autodependogram is based on the simple idea of using, instead of autocorrelations at varying time lags, the chi-square test statistics applied to convenient contingency tables. The efficacy of this graphical device is confirmed by real and artificial time series and by simulations from certain classes of well-known models, characterized by randomness and by different kinds of linear and nonlinear dependences.