In this paper we present an unsupervised time series anomaly detection algorithm, which is based on the discrete wavelet transform (DWT) operating fully online. Given streaming data or time series, the algorithm iteratively computes the (causal and decimating) discrete wavelet transform. For individual frequency scales of the current DWT, the algorithm estimates the parameters of a multivariate Gaussian distribution. These parameters are adapted in an online fashion. Based on the multivariate Gaussian distributions, unusual patterns can then be detected across frequency scales, which in certain constellations indicate anomalous behavior. The algorithm is tested on a diverse set of 425 time series. A comparison to several other state-of-the-art online anomaly detectors shows that our algorithm can mostly produce results similar to the best algorithm on each dataset. It produces the highest average F1-score with one standard parameter setting. That is, it works more stable on high- and low-frequency-anomalies than all other algorithms. We believe that the wavelet transform is an important ingredient to achieve this.