In this paper, we developed and applied a stochastic model based on a discrete-time semi-Markov chain approach and its generalizations to study the high-frequency price dynamics of traded stocks. Semi-Markov is a stochastic process that generalizes both the Markov chain and the Markov renewal processes. It is well known that the performances of the stock market or factors that move stock prices are technical factors, fundamental factors, and market sentiments. The discrete-time semi-Markov model is applied on stock values of capital assets for both opening and closing prices for a specific period to predict the long-term behavior of the stock value price movement for the three states (bull market state, bear market state, and stagnant market state) for the process. The daily closing prices of stocks depend on the subsequent daily closing prices and there is a hope of recovering for capital asset stocks after the experience of unprecedented losses in stock values during the previous years. From the long run probabilities, the results showed that the probability of stock prices either increasing or decreasing is higher than being stable. So there is a high likelihood that stocks will not be stable in the long run. Thus, it is an indication that there is a high tendency for stock prices to fluctuate in the future than being stable.

discrete-time semi-Markov model, stock prices, bull market, bear market, stagnant market.

Received: July 9, 2021; Accepted: August 18, 2021; Published: November 15, 2021

How to cite this article: Mamadou Alieu Jallow, Patrick Weke, Lukman Abiodun Nafiu and Carolyne Ogutu, Application of a discrete-time semi-Markov model to the stochastic forecasting of capital assets as stock, Far East Journal of Theoretical Statistics 63(1) (2021), 1-18. DOI: 10.17654/TS063010001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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