Abstract: This study examined the annual profit after tax (PAT) generated by 22 December ending fiscal year firms quoted on the Nigerian Stock Exchange from the early 1970s to 2011. The stochastic processes of each firms PAT were examined with a view to determining whether they are stationary or nonstationary, using the Augmented Dickey-Fuller statistic. The Ljung-Box portmanteau statistic was also used to determine whether or not the error terms displayed by the correlogram of each of the firms are white noise. Examination of the pattern of PAT of the firms showed that less than a third of them could realize consistently positive profits during the study period. In determining the appropriate model for each firm's PAT, the Schwartz's Bayesian Information Criterion was used and it was found that the model obtained for most of the firms is autoregressive integrated (ARI) while a third of the models are autoregressive integrated moving average (ARIMA). Based upon the findings in the study, it is recommended that the federal government should endeavour to pursue good macroeconomic policies which would assist Nigerian quoted firms to increase the regularity of earning positive profits after tax over time.