Analysis of Exchange Rates as Time‐Inhomogeneous Markov Chain with Finite States

Irrespective of whether the test for homogeneity is significant or not, most researchers assume time‐homogeneity in analysing Markov chains due to scanty literature on the analysis of time‐inhomogeneous Markov chains. Based on the assumption that, for each point in time in the future, a stochastic process will be subjected to a randomly selected transition matrix from an ergodic set of transition matrices the process was subjected to in the recent past, a methodology was proposed for analysing the long‐run behaviours of time‐inhomogeneous Markov chains. The proposed model was implemented to historical data consisting of the exchange rate of cedi‐dollar, cedi‐pound, and cedi‐euro spanning over 6 years (January 2012 to December 2017). The results show that under certain “closeness” conditions, the long‐run behaviours of the time‐inhomogeneous case are almost identical to those of the time‐homogeneous case. The paper asserted that even if the Markov chain exhibit time‐inhomogeneity, analysing the Markov chain under the assumption of time‐homogeneity is a step in the right direction under certain “closeness” conditions; otherwise, the proposed method is recommended. It was also found that investing in dollars yields better returns than the other currencies in Ghana.