In this paper we give a geometrical interpretation of regime-switching models when the changing mechanism between the states is governed by an unobservable Markov process. In particular we consider a stochastic two-regimes model of price behaviour with time-varying parameters and we prove that the space of the conditional probability distributions is an exponential family where the information at the previous time is an hidden variable. Analogously to the neural case, we obtain a network trained by various input signals and corresponding output behaviours. This mechanism has been identified as the universal way for the transfer of the information. We also deduce that in this case (EM) and (em) algorithms of Information Geometry are equivalent.
Information Geometry of a Regime-Switching Model with timevrying parameters
DE SANCTIS, Angela Anna
2010-01-01
Abstract
In this paper we give a geometrical interpretation of regime-switching models when the changing mechanism between the states is governed by an unobservable Markov process. In particular we consider a stochastic two-regimes model of price behaviour with time-varying parameters and we prove that the space of the conditional probability distributions is an exponential family where the information at the previous time is an hidden variable. Analogously to the neural case, we obtain a network trained by various input signals and corresponding output behaviours. This mechanism has been identified as the universal way for the transfer of the information. We also deduce that in this case (EM) and (em) algorithms of Information Geometry are equivalent.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
