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

Abstract

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.

Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations

“…Similar to the method of the problem (11), we obtain the eigenvalue 1 2 , r at r at      of the homogeneous equation of (13). Assuming that the solution of (13) is…”

“…(a) Simulated music (b) Original music Figure 4 Overall Spectrogram of Music Signal Time Series (2) It is imperative to examine the contribution rate of various frequencies in the time series of music signals in different periods. We performed the Fourier transform of each vibration peak period in the music signal time series [11]. Figure 5 presents the spectrograms of the fifth vibration peak cycle in the original and analog music signal time series.…”