Side-Length-Independent Motif ( SLIM ): Motif Discovery and Volatility Analysis in Time Series— SAX , MDL and the Matrix Profile

As the availability of big data-sets becomes more widespread so the importance of motif (or repeated pattern) identification and analysis increases. To date, the majority of motif identification algorithms that permit flexibility of sub-sequence length do so over a given range, with the restriction that both sides of an identified sub-sequence pair are of equal length. In this article, motivated by a better localised representation of variations in time series, a novel approach to the identification of motifs is discussed, which allows for some flexibility in side-length. The advantages of this flexibility include improved recognition of localised similar behaviour (manifested as motif shape ) over varying timescales. As well as facilitating improved interpretation of localised volatility patterns and a visual comparison of relative volatility levels of series at a globalised level. The process described extends and modifies established techniques, namely SAX , MDL and the Matrix Profile, allowing advantageous properties of leading algorithms for data analysis and dimensionality reduction to be incorporated and future-proofed. Although this technique is potentially applicable to any time series analysis, the focus here is financial and energy sector applications where real-world examples examining S&P500 and Open Power System Data are also provided for illustration.