Most state-of-the-art action feature extractors involve differential operators, which act as highpass filters and tend to attenuate low frequency action information. This attenuation introduces bias to the resulting features and generates ill-conditioned feature matrices. The Gaussian Pyramid has been used as a feature enhancing technique that encodes scale-invariant characteristics into the feature space in an attempt to deal with this attenuation. However, at the core of the Gaussian Pyramid is a convolutional smoothing operation, which makes it incapable of generating new features at coarse scales. In order to address this problem, we propose a novel feature enhancing technique called Multi-skIp Feature Stacking (MIFS), which stacks features extracted using a family of differential filters parameterized with multiple time skips and encodes shift-invariance into the frequency space. MIFS compensates for information lost from using differential operators by recapturing information at coarse scales. This recaptured information allows us to match actions at different speeds and ranges of motion. We prove that MIFS enhances the learnability of differential-based features exponentially. The resulting feature matrices from MIFS have much smaller conditional numbers and variances than those from conventional methods. Experimental results show significantly improved performance on challenging action recognition and event detection tasks. Specifically, our method exceeds the state-of-the-arts on Hollywood2, UCF101 and UCF50 datasets and is comparable to state-of-the-arts on HMDB51 and Olympics Sports datasets. MIFS can also be used as a speedup strategy for feature extraction with minimal or no accuracy cost.