In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes . The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the 'best model' for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the 'best model'.