Abstract: This study used wavelet analysis to detect Anomalous Observations (AOs) in non-stationary and non-periodic simulated data while extending it to the parametric method using a developed test statistic. In the three series analysed, it was discovered that Turkey’s method (TM), the Modified Turkey’s method (MTM) and the developed test statistic were found to be very effective and efficient in the detection of these anomalous observations even when the data are compressed, they still retained their statistical properties .