MARKOV MODELS FOR THE ANALYSIS OF DYNAMICAL SYSTEMS

Abstract

Most real world situations involve modelling of physical processes that evolve with time and space, especially those exhibiting high variability. Such events that have to flow with time or space are called dynamical systems. The mathematical notions of a dynamical system serves to depict the flow of causation from past into future (Kalman 1960). In this study, Markov model which is a signal model based on the Markovian property with state space approach was adopted for the analysis of dynamical systems. The Nigerian monetary exchange rate data was used in the application with the use of R statistical software package. The study incorporated the Chapman-Kolmogorov equation in the construction of absolute limiting distribution of the system via the state variables. The procedure gives an easy and effective means of analysing complex and time varying dynamical systems. The study showed that the Nigerian monetary exchange rate is ergodic with stationary probability distribution.