Title: Window Projection Features are All You Need for Time Series Anomaly Detection. Abstract: The challenge of time series anomaly detection has motivated the development of increasingly more complex deep representations and anomaly metrics. In this paper we demonstrate that a simple approach based on window projection features can achieve better results. Projection features are a common way to discretize multivariate data; they first multiply the data by a projection matrix followed by discretization of each output dimension. We first show that short temporal windows, encoded by projection features, are often already sufficiently expressive for linearly separating between normal and anomalous time series. However, we find that while the expressivity of projection features is sufficient, current one-class classification methods are unable to use them effectively to detect anomalies. We hypothesize this is due to the difficulty of density estimation. The difficulty can be overcome by estimating the probability density of the sample mean, which follows the Gaussian distribution when the conditions of the Central Limit Theorem are met. Simply put, we fit a multivariate Gaussian model to the average of the projection features of adjacent windows within a time series. Despite its simplicity, our method outperforms the state-of-the-art in diverse settings including: five UEA datasets, video trajectory anomaly detection and standard anomaly segmentation benchmarks. Code is provided.