Subspace representations that preserve essential information of high-dimensional data may be advantageous for many reasons such as improved interpretability, overfitting avoidance, acceleration of machine learning techniques. In this article, we describe a new subspace representation of time series which we call polynomial shape space representation. This representation consists of optimal (in a least-squares sense) estimators of trend aspects of a time series such as average, slope, curve, change of curve, etc. The shape space representation of time series allows for a definition of a novel similarity measure for time series which we call shape space distance measure. Depending on the application, time series segmentation techniques can be applied to obtain a piecewise shape space representation of the time series in subsequent segments. In this article, we investigate the properties of the polynomial shape space representation and the shape space distance measure by means of some benchmark time series and discuss possible application scenarios in the field of temporal data mining.