A sequential Monte Carlo (SMC) algorithm prediction approach is developed based on joint probability distribution in hidden Markov Models (HMM). SMC methods, a general class of Monte Carlo methods, are typically used for sampling from sequences of distributions and simple examples of these algorithms are found extensively throughout the tracking and signal processing literature. Recent developments indicate that these techniques have much more general applicability and can be applied very effectively to statistical inference problems. Due to the problem involved in estimating the parameter of HMM, the HMM is represented in a state space model and the sequential Monte Carlo (SMC) method is used. Predictions are made using the SMC method in HMM and the corresponding on-line algorithm is developed. Daily stock price data from the banking sector of the Nigerian Stock Exchange (NSE) (price index between the years 1 January 2005 to 31 December 2008) are analyzed; experimental results reveal that the method proposed is effective.