Abstract
The study aimed at stabilizing the changing variance using the logarithmic transformation to achieve a significant proportion of stability and a faster rate of convergence of the steady state transition probability in Markov chains. The traditional Markov chain and logarithmic-modified Markov chain were considered. On exploring the yearly data on the stock prices from 2015 to 2018 as obtained from the Nigerian Stock Exchange, it was found that the steady state of logarithmic-modified Markov chain converged faster than the tradition Markov chain with efficiency in tracking the correct cycles where the stock movements are trending irrespective of which cycle it starts at time zero with differences in probability values by 1.1%, 0.7%, −0.41% and −1.37% for accumulation, markup, distribution and mark-down cycles, respectively. Thus, it could be deduced that the logarithmic modification enhances the ability of the Markov chain to tract the variation of the steady state probabilities faster than the traditional counterpart.
Highlights
In Statistics, trends are steady and methodical fluctuations in the variance of a process over a long period of time and their underlying features are embedded with useful information that are viable for investment decisions [1⚶4]
The striking reason for continuous application of Markov chains in investment trend analysis is the existence of a limiting probability distribution which is independent of initial states, and this is associated with the convergence in probability of finding the Markov chain in a particular state irrespective of which state the chain began at time zero
Given the fact that Markov chain models are appropriate in tracking long-run behavior of trends but failed in tracking short-term behavior prompted the studies of [11⚶15] to provide the missing link
Summary
In Statistics, trends are steady and methodical fluctuations in the variance of a process over a long period of time and their underlying features are embedded with useful information that are viable for investment decisions [1⚶4]. The striking reason for continuous application of Markov chains in investment trend analysis is the existence of a limiting probability distribution which is independent of initial states, and this is associated with the convergence in probability of finding the Markov chain in a particular state irrespective of which state the chain began at time zero. Prior studies such as [7⚶10] applied Markov chain model approach to analyze and forecast stock trends. Given the fact that Markov chain models are appropriate in tracking long-run behavior of trends but failed in tracking short-term behavior prompted the studies of [11⚶15] to provide the missing link
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