CURVED CHAOTIC MAP TIME-SERIES MODELS AND THEIR STOCHASTIC REVERSALS

This paper considers two types of chaotic map time series models, incl uding the well-known tent, logistic and binary-shift maps as special c ases; these are called curved tent and curved binary families. Determi nistic behaviour is investigated by invariant distributions, Lyapunov exponents, and by serial dependency. Stochastic time reversal of the f amilies is shown to produce models which have a broader range of stoch astic and chaotic properties than their deterministic counterparts. Th e marginal distributions may have concentrations and restricted suppor ts and are shown to be a non-standard class of invariant distribution. Dependency is generally weaker with the reversed stochastic models. T he work gives a broad statistical account of deterministic and stochas tically reversed map models, such as are emerging in random number gen eration, communication systems and cryptography.