Financial Time Series: Motif Discovery and Analysis Using VALMOD

Abstract

Motif discovery and analysis in time series data-sets have a wide-range of applications from genomics to finance. In consequence, development and critical evaluation of these algorithms is required with the focus not just detection but rather evaluation and interpretation of overall significance. Our focus here is the specific algorithm, VALMOD , but algorithms in wide use for motif discovery are summarised and briefly compared, as well as typical evaluation methods with strengths. Additionally, Taxonomy diagrams for motif discovery and evaluation techniques are constructed to illustrate the relationship between different approaches as well as inter-dependencies. Finally evaluation measures based upon results obtained from VALMOD analysis of a GBP-USD foreign exchange (F/X) rate data-set are presented, in illustration.

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

“…In the energy sector, a set of hourly Open Power System Data (OPSD) relevant for power system modelling within the EU and neighbouring countries was considered [39]. For the financial illustration, we build upon previous work [36,37] and continue with S&P500 data, as it is widely regarded as the best single gauge of U.S. equities and serves as the foundation for a wide range of investment products [40].…”

“…For time series, MDL-SAX compression of the original SAX string has the net effect of 'removing' periods of stability while retaining the volatility profile (Figure 6a). Figure 6 illustrates a comparison between SAX and MDL-SAX representations of the S&P500 from January 2008 to January 2010, a window chosen for the volatility that reflects the considerable stress experienced in the global marketplace at this time [34,35] and extending previous work [36,37] In the illustrated example, the MDL-SAX and SAX strings are plotted using both non-adjusted (Figure 6a) and adjusted (Figure 6b) scales to highlight the features of the SAX string captured by MDL-SAX. The overall shape and dynamics are well preserved, as the series examined has relatively few periods of stability.…”

NATSA: A Near-Data Processing Accelerator for Time Series Analysis

“…The algorithm addresses the imposed data dependency due to the dot product update between the elements in the diagonal with the following steps: 1) it pre-computes the add terms in Eq. 2 in batches of size vectF actor in a vectorized manner (lines 13-14); 2) it adds the previous dot product to the rst new one (line 15); 3) it sequentially updates the remaining dot products in the batch (lines [16][17] saving the last one for the next iteration of the diagonal (line 18); 4) it computes the distance as well as the pro le update in a vectorized way (lines [19][20][21][22]. As a result, all loops are fully vectorized except the one in lines 16-17.…”

“…NATSA is motivated by two key observations: First, time series motif and discord discovery are two of the most important analysis primitives for a wide variety of applications. Besides the applications mentioned in Section 1, we can nd these primitives applied to bioinformatics [8,10,14], speech processing [32], robotics [80], weather prediction [64], entomology [97], geophysics [21], nance [20], communication engineering [54], and electroencephalography [45].…”

Financial Time Series: Market Analysis Techniques Based on Matrix Profiles †

“…Among the motif discovery algorithms that we have investigated [8,9], a new data construct based upon an efficient nearest neighbours discovery method and designated as the Matrix Profile (MP) [10] has already clearly demonstrated considerable potential for its extension and flexibility of application. Thus, we are less concerned here with the relative superiority of the MP on a point-by-point basis as compared to other motif discovery algorithms, but rather a demonstration of how visual tools, namely MP plots, can provide insight on single and multiple financial series data and their macro-economic interpretation.…”