Testing for Markovian Property: A Statistical Approach to Transition Matrix Homogeneity

Abstract

Markov chains are powerful tools for modeling systems that transition between distinct states with the probability of transitioning to each state depending solely on the previous one. This Markov property is central to applications across disciplines, including geology, biology, and economics, as it allows for simplified, tractable analysis. In this paper, we assess the presence of Markovian behavior in several processes by estimating a one-step transition probability matrix and employing a chi-squared test to validate the consistency of transition probabilities over time. Using R software, our study also examines change-point detection to identify shifts in transition matrices, offering insights into cases where Markovian assumptions may or may not hold, such as weather patterns, language structures, and stock price movements.