High-dimensional time series data poses challenges due to its dynamic nature, varying lengths, and presence of missing values. This kind of data requires extensive preprocessing, limiting the applicability of existing Time Series Classification and Time Series Extrinsic Regression techniques. For this reason, we propose BORF, a Bag-Of-Receptive-Fields model, which incorporates notions from time series convolution and 1D-SAX to handle univariate and multivariate time series with varying lengths and missing values. We evaluate BORF on Time Series Classification and Time Series Extrinsic Regression tasks using the full UEA and UCR repositories, demonstrating its competitive performance against state-of-the-art methods. Finally, we outline how this representation can naturally provide saliency and feature-based explanations.