Monthly All Share Index data from 1985M01-2021M12 was sourced from the Central Bank of Nigeria and the Central Securities Clearing System of the Nigerian Stock Exchange; to analyze multiple bubble periods. The supremum Augmented Dickey Fuller (SADF) and Generalized supremum Augmented Dickey Fuller (GSADF) quantitative model with 1000 repetitions along with a window size of 42 was selected to carry out the Monte Carlo simulation at the 95% confidence level. From the Backward SADF estimation, three periods of explosive pricing and collapses were detected. The study therefore recommends that market regulators should promote market information and support regular training of market participants to stem speculations and reduce arbitrage. Overall, well-informed risk management practices should be established to guard against market losses.