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Several high level representations of time series have been proposed in the research literature, including Fourier Transforms (Keogh et al., 2000), Wavelets (Chan & Fu, 1999), Symbolic Mappings (Das, Lin, Mannila, Renganathan, & Smyth, 1998; Perng et al., 2000) and Piecewise Linear Approximation or PLA: (Chan & Fu, 1999; Ge & Smyth, 1999; Hunter & McIntosh, 1998; Junker, Amft, Lukowicz, & Tröster, 2008; Keogh et al., 2004; Lavrenko, Schmill, Lawrie, Ogilvie, Jensen, & Allan, 2000; Li, Yu, & Castelli, 1998; Osaki, Shimada, & Uehara, 1999; Park, Lee, & Chu, 1999; Qu, Wang, & Wang, 1998; Shatkay & Zdonik, 1996; Vullings, Verhaegen, & Verbruggen, 1997; Wang & Wang, 2000).
Key Terms in this Chapter
Financial Index: A time dependent indicator used to measure and report value changes in a selected group of stocks.
Big Data: Big data usually includes data sets with sizes beyond the ability of commonly-used software tools to capture, curate, manage, and process the data within a tolerable elapsed time.
Segmentation: Segmentation refers to the automatic process of partitioning a data stream into multiple segments by set of predefined features (e.g. temperature, electricity consumptions, workdays, etc.).
Data Stream: Data stream is time series sequence which flows into a computer system continuously, in a non-stationary way and with varying update rates. Often, it may be impossible to store an entire data stream or to scan through it multiple times due to its tremendous volume.
Stationarity: A statistical characteristic of a time series for which the distribution does not change over time.
Time Series: A series of values of a quantity obtained at successive times, often with equal intervals between them.
Sliding Window: Sliding (Rolling) window refers to looking at a subset of points in the time series rather than all previous points. This “window” consecutively rolls back, holding the same number of points within the window as it moves along the time series data streams.