Sparse approximation is a novel technique in applications of event detection problems to long-term complex biomedical signals. It involves simplifying the extent of resources required to describe a large set of data sufficiently for classification. In this paper, we propose a multivariate statistical approach using dynamic principal component analysis along with the non-overlapping moving window technique to extract feature information from univariate long-term observational signals. Within the dynamic PCA framework, a few principal components plus the energy measure of signals in principal component subspace are highly promising for applying event detection problems to both stationary and non-stationary signals. The proposed method has been first tested using synthetic databases which contain various representative signals. The effectiveness of the method is then verified with real EEG signals for the purpose of epilepsy diagnosis and epileptic seizure detection. This sparse method produces a 100% classification accuracy for both synthetic data and real single channel EEG data.