Analysis and prediction of chaos in rainfall and stream flow time series

Abstract

The time delay embedding method of reconstructing the phase-space diagram of a time series is examined for uncovering possible chaotic behaviour and making non-linear predictions. The reliability of the various parameters that characterise chaotic time series are verified using artificially generated data from random, Autoregressive Moving Average (ARMA) and chaotic series with additive noise. Non-linear predictions are made using a local approximation method and applied to some daily rainfall and stream flow data in Hong Kong. There is convincing statistical evidence to believe that the stream flow and rainfall data series are better modelled by the time delay embedding approach than by the traditional linear ARMA approach.