Multivariate time series anomaly detection is a crucial problem in many industrial and research applications. Timely detection of anomalies allows, for instance, to prevent defects in manufacturing processes and failures in cyberphysical systems. Deep learning methods are preferred among others for their accuracy and robustness for the analysis of complex multivariate data. However, a key aspect is being able to extract predictions in a timely manner, to accommodate real-time requirements in different applications. In the case of deep learning models, model reduction is extremely important to achieve optimal results in real-time systems with limited time and memory constraints. In this paper, we address this issue by proposing a novel compression method for deep autoencoders that involves three key factors. First, pruning reduces the number of weights, while preventing catastrophic drops in accuracy by means of a fast search process that identifies high sparsity levels. Second, linear and non-linear quantization reduces model complexity by reducing the number of bits for every single weight. The combined contribution of these three aspects allow the model size to be reduced, by removing a subset of the weights (pruning), and decreasing their bit-width (quantization). As a result, the compressed model is faster and easier to adopt in highly constrained hardware environments. Experiments performed on popular multivariate anomaly detection benchmarks, show that our method is capable of achieving significant model compression ratio (between 80% and 95%) without a significant reduction in the anomaly detection performance.