The usefulness of wavelet transform and wavelet filtering techniques for the improvement of the estimation of the decay ratio (DR), characterising the stability of BWRs, is discussed. There are two distinct areas investigated. The first concerns the improvement of the quality of the traditionally used auto-correlation function (ACF) for the estimation of the DR, by trend elimination and denoising. The subsequent estimation of the DR itself is made by traditional methods such as the peak-to-peak method or curve fitting. The second area is the estimation of the DR by the use of continuous wavelet transform. The possibility of estimating two different DRs in case of dual oscillations, and in particular the finding of the higher DR, is also investigated. It was found that wavelet pre-processing does not always improve the estimation of the ACF of a non-ideal signal, compared to other methods; but for signals containing various trends and data scatter in the ACF, it brings a noticeable improvement. As an extension of the discrete wavelet methods, the continuous wavelet transform appears to be a promising candidate to determine the critical DR even in the case of two oscillations being co-existent with different stability properties. The methods investigated or developed here were also tested on measured data from Swedish BWRs.