Time series (TS) data have consistently been in short supply, yet their demand remains high for training systems in prediction, modeling, classification, and various other applications. Synthesis can serve to expand the sample population, yet it is crucial to maintain the statistical characteristics between the synthesized and the original TS : this ensures consistent sampling of data for both training and testing purposes. However the time domain features of the data may not be maintained. This motivates for our work, the objective which is to preserve the following features in a synthesized TS: its fundamental statistical characteristics and important time domain features like its general shape and prominent transients. In a novel way, we first isolate important TS features into various components using a spectrogram and singular spectrum analysis. The residual signal is then randomized in a way that preserves its statistical properties. These components are then recombined for the synthetic time series. Using accelerometer data in a clinical setting, we use statistical and shape measures to compare our method to others. We show it has higher fidelity to the original signal features, has good diversity and performs better data classification in a deep learning application.