Moving Approximation Transform and Local Trend Associations in Time Series Data Bases

Transcribing Debussy's Syrinx dynamics through Linguistic Description: The MUDELD algorithm

“…Alternatively to statistical studies, Batyrshin et al [18] advocated for the extraction of rule-based descriptions of time series using linguistic shape descriptors. Chiang, Chow and Wang [19] proposed a novel method for mining time series capable of overcoming the problem of having points very close or even equal to each other.…”

Up and Down Trend Associations in Analysis of Time Series Shape Association Patterns

“…Another example of time series shape association measure gives the trend association measure based on moving approximation transform [3]. Consider time series from T n .…”

“…But there are many economical, financial, industrial, ecological systems that contain changing in time elements or characteristics such that an increase in the values of the one of them happens together with a decrease in the values of another one: prices and sales, the sales volumes of competitive companies, the wind velocity and air pollution concentration etc. In [4] it was pointed out that correlation coefficient and trend association measure based on moving approximation transform [3] satisfy axioms of shape association measures and can be used for measuring possible direct and inverse relationships between time series and time series patterns. In presented work a new measure of time series shape associations is introduced that can be used for recognition of time series shape association patterns both with direct and inverse possible relationships.…”

Positive and Negative Local Trend Association Patterns in Analysis of Associations between Time Series

“…In [3][4], it was pointed out a need in the measures of associations between time series that additionally to similarity between time series could measure inverse relationships between them. Additionally to considered above examples such measures could be used for finding sequences of competitive companies or products with inverse patterns when the rising patterns of one sequence correspond to falling patterns of another one.…”

“…Additionally to considered above examples such measures could be used for finding sequences of competitive companies or products with inverse patterns when the rising patterns of one sequence correspond to falling patterns of another one. In [3], the measures of local trend associations (LTA) based on Moving Approximation Transform (MAT) have been introduced and examples of their application to analysis of possible relationships between elements of economic and financial systems have been considered. In [5], the method of construction of positive and negative local trend association patterns for any pair of time series based on MAT with window size k=2 has been proposed.…”