Abstract:
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.
