Neuromorphic event-based dynamic vision sensors (DVS) have much faster sampling rates and a higher dynamic range than frame-based imaging sensors. However, they are sensitive to background activity (BA) events that are unwanted. There are some filters for tackling this problem based on spatio-temporal correlation. However, they are either memory-intensive or computing-intensive. We propose \emph{SeqXFilter}, a spatio-temporal correlation filter with only a past event window that has an O(1) space complexity and has simple computations. We explore the spatial correlation of an event with its past few events by analyzing the distribution of the events when applying different functions on the spatial distances. We find the best function to check the spatio-temporal correlation for an event for \emph{SeqXFilter}, best separating real events and noise events. We not only give the visual denoising effect of the filter but also use two metrics for quantitatively analyzing the filter's performance. Four neuromorphic event-based datasets, recorded from four DVS with different output sizes, are used for validation of our method. The experimental results show that \emph{SeqXFilter} achieves similar performance as baseline NNb filters, but with extremely small memory cost and simple computation logic.