A Comparative Analysis of Continuous-time Markov Chain, Logistic Regression and F-Distribution-Based Inference in Modelling Share Price Movement Dynamics of Fidelity Bank Plc

This study examines the dynamics of the share price of Fidelity Bank Plc through three complementary statistical tools: a continuous-time Markov chain (CTMC), logistic regression and inference based on Snedecor’s F-distribution. The analysis uses the matrix of transition counts among three price-movement states (decrease, increase and no change) reported for closing prices from 1 April 2016 to 23 March 2022, comprising 1,481 transitions. The transition probability matrix is estimated by maximum likelihood, with exact Clopper–Pearson limits computed from F quantiles, and a valid CTMC generator is obtained as the matrix logarithm of the estimated matrix. Decreases and unchanged prices were persistent (the probabilities of remaining in the same state were 0.675 and 0.637, respectively), whereas increases were less persistent (0.460). The stationary distribution was 0.415, 0.178 and 0.407 for decrease, increase and no change; the mean sojourn times were 3.08, 1.85 and 2.75 observations. A chi-square test rejected independence of consecutive states (χ²(4) = 450.97, p < 0.001; Cramér’s V = 0.390). Logistic regression showed that the odds of a price change were 5.28 times higher (95% CI 4.21–6.61) after a price change than after an unchanged price, and that the direction of a move tended to repeat that of the preceding move. The results describe persistence in price-movement activity and direction; they do not measure the magnitude of volatility, which requires dated return series.