Share Price Prediction Using Markov Chain Modelling and Principal Component Analysis for Stock Market Capitalisation
DOI:
https://doi.org/10.63561/jmns.v2i4.1123Keywords:
Stochastic analysis, Markov chain, Share price, Market Capitalization, Transition matrix, PCAAbstract
Investors in the financial market are frequently confronted with critical decisions regarding the allocation of funds for the purpose of optimal profit returns. This is largely due to its stochastic nature. This study is centred on analysing this stochastic behaviour for optimal investment decisions. The Markov chains and Principal Component Analysis (PCA) were applied to the closing share price data of two Nigerian banks - Access and Fidelity Banks. Their share prices were transformed into a 3-step transition probability matrix solution, spanning several years, to accurately predict future changes in share prices. The PCA results showed that the first and second PCA values are similar for both banks, suggesting that the factors that affect share price are similar for both banks. The small difference in the values indicates that some specific factors affect one bank more than the other, but overall, they are influenced by similar factors. This information is useful for investors deciding between the two banks, as it suggests that their risk and return profiles are similar. All numerical examples were generated using MATLAB.
References
Adeosun, M.E., Edeki, S.O., & Ugbebor, O.O. (2015). Stochastic analysis of stock market price models: A case study of the Nigerian stock exchange (NSE). WSEAS transactions on Mathematics,14,353-363.
Agbam, A.S., & Udo, E.O.(2020). Application of markov chain model to stochastic forecasting of stock prices in Nigeria: the case study of Dangote cement. International Journal of Applied Science and Mathematical Theory, 6(1).
Agwuegbo, S.O. N., Adewole, A.P., & Maduegbuna, A.N. (2010). A random walk for stock market prices. Journal of Mathematics and Statistics, 6(3), 342-346.
Amadi, I. U., & Victor-Edema, U. A. (2025). Stochastic model on share price movements in finite state with asymptotic null controllability property
Amadi, I. U., Ogbogbo, C.P., & Osu, B.O. (2022a).Stochastic analysis of stock price changes as Markov chain in finite states, Global Journal of Pure and Applied Sciences, 28, 91-98.
Amadi, I. U., Igbudu, R., & Azor, P. A.(2022b). Stochastic analysis of the impact of growth-rates on stock market prices. Asian Journal of Economic, Business and Accounting.
Lakshmi, G.J.M., & Jyothi, M.(2020). Application of Markov process for prediction of stock market performance. International Journal of Recent Technology and Engineering, 8(6).
Bairagi, A., & Kakaty, S. (2015). Analysis of stock market price behaviour: A Markov chain approach. International Journal of Recent Scientific Research, 6(10), 7061-7066.
Christian, E.O., & Timothy, K.S. (2014). On predicting the long run behaviour of Nigerian bank stock prices: a Markov chain approach. American Journal of Applied Mathematics and Statistics,4(4), 212-215.
Davies, I. Amadi, I.U., & Ndu, R.I. (2019). Stability analysis of stochastic models for stock market prices. International Journal of Mathematics and Computational Methods,4,79-86.
Davou, N.C, Samuel, N.E., & Gokum, T.K.(2013). Markov chain model application on share price movement in stock market. Computer Engineering and Intelligent Systems,4(10).
Eseoghene, J.I. (2011). The long run prospect of stocks in the Nigerian capital market: a Markovian analysis. Journal of Research in National Development, 9(1).
Mettle, F.O, Quaye, E.N.B., & Laryea, R.A. (2014). A methodology for stochastic analysis of share prices as Markov chains with finite states. http://www.springerplus.com/content/3/1/057.
Ofomata, A.I.O., Inyama, S.C., Umana, R.A., & Omane, A.O. (2017). A stochastic model of the dynamics of stock price for forecasting. Journal of Advances in Mathematics and Computer Science, 25(6),1-24.
Osu, B.O., Emenyonu, S.C ., Ogbogbo, C.P., & Olunkwa, C. (2019). Markov models on share price movements in Nigeria stock market capitalization, Applied Mathematics and Information Sciences, an International Journal,2,1-9.
Udom, A.U. (2015). Elements of applied mathematical statistics. Second Edition, University of Nigeria Press Limited.
Ugbebor, O.O., Onah, S.E., & Ojowo, O.(2001). An empirical stochastic model of stock price changes. Journal Nigerian Mathematical Society,20, 95-101
Zhang D., & Zhang X. (2009).Study on forecasting the stock market trend based on a stochastic analysis method. International Journal of Business and Management. 4(6). 163-170.
