On the Discovery of Weak Periodicities in Large Time Series

Abstract

The search for weak periodic signals in time series data is an active topic of research. Given the fact that rarely a real world dataset is perfectly periodic, this paper approaches this problem in terms of data mining, trying to discover weak periodic signals in time series databases, when no period length is known in advance. In existing time series mining algorithms, the period length is user-specified. We propose an algorithm for finding approximate periodicities in large time series data, utilizing autocorrelation function and FFT. This algorithm is an extension to the partial periodicity detection algorithm presented in a previous paper of ours. We provide some mathematical background as well as experimental results.

Discovering Partial Periodic Patterns in Discrete Data Sequences

“…Our method is more efficient than the circular autocorrelation method in [1] because of the following reasons: (1) We compute F 1 during the period discovery process in one pass. (2) Our method works well even when the length of data sequence n is unknown in advance.…”

“…E.g., in the symbol sequence "abababab", the subsequence "ab" is a periodic pattern. Since periodic patterns show trends in time series or event sequences, the problem of mining partial periodic patterns has been studied in the context of time series and event sequence databases ( [1]- [3]). …”

“…This method outperforms the Apriori-like algorithm, but it assumes that the periods are given in advance, which limits its applicability. Berberidis et al [1] has proposed a method that finds periods for which a data sequence may contain patterns. However, this method may miss some frequent periods and it requires a separate pass to scan the data sequence to compute the periods.…”

Anomaly detection in SCADA systems : a network based approach

“…The limitation of having the periods to be known in advanced is addressed in more recent works [19,26].…”

“…Berberidis et al [19] extend the approach by adding a pre-processing filter step, where the ACF is used to estimate a set of possible periods for each symbol in the alphabet. The algorithm proposed by Han and Yin [72] is then applied to each of these periods.…”