Time series recorded by acoustic velocimeters are often affected by a combination of factors, including turbulent velocity fluctuations, Doppler noise and signal aliasing. Although it is not possible to find a comprehensive threshold for identifying spurious data, the present work attempts to describe an effective technique for detecting spikes. This technique is based on transforming data into wavelet space and thresholding the wavelet basis by a consistent threshold. The universal threshold modified by a robust scale estimator such as Qn is proven to work extremely well. The suggested methods for replacing identified spikes combine times series analyses (linear time series modelling or a Kalman predictor) with a straightforward method, polynomial interpolation, to generate substitutions retaining both the trends and the fluctuations in the surrounding clean data. Then, tests were performed to reveal the influence of replacing methods on the total number of detected spikes, required iterations and physical properties of the restored signal. From the overall results, it is inferred that using the wavelet-Qn as the detecting module and integrating it with linear time series modelling/Kalman filtering as the replacement module constitutes an effective despiking algorithm. This methodology is capable of restoring the contaminated signal in such a way that its statistical and physical properties correlate well with those of the original record.