Summary: A wavelet-based technique is proposed for analysing localized significant changes in observed data in the presence of noise. The main tasks of the proposed technique are
(a) denoising the observed data without removing localized significant changes,
(b) classifying the detected sharp jumps (spikes), and
(c) obtaining a smooth trend (deterministic function) to represent the time-series evolution.
By using the Haar discrete wavelet transform, the sequence of data is transformed into a sequence of wavelet coefficients. The Haar wavelet coefficients, together with their rate of change, represent local changes and local correlation of data; therefore, their analysis gives rise to multi-dimensional thresholds and constraints which allow both the denoising and the sorting of data in a suitable space.