The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and taking estimation into account via the Sequential Monte Carlo Expectation Maximisation (SMCEM) technique, this study finds no support of randomness. In conclusion, the stock price movements of the NSE do not follow the random walk process