The raining of periodic patterns in time series databases is an interesting data mining problem that can be envisioned as a tool for forecasting and predicting the future behavior of time series data. Existing periodic patterns mining algorithms either assume that the periodic rate (or simply the period) is user-specified, or try to detect potential values for the period in a separate phase. The former assumption is a considerable disadvantage, especially in time series databases where the period is not known a priori. The latter approach results in a multi-pass algorithm, which on the other hand is to be avoided in online environments (e.g., data streams). In this paper, we develop an algorithm that mines periodic patterns in time series databases with unknown or obscure periods such that discovering the period is part of the mining process. Based on convolution, our algorithm requires only one pass over a time series of length n, with O(n log n) time complexity.
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