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

Abstract

The method of recognition of shape association patterns with direct and inverse relationships is proposed. This method is based on a new time series shape association measure based on Up and Down trend associations. The application of this technique to analysis of associations between well production data in petroleum reservoirs is discussed.

Constructing Time Series Shape Association Measures: Minkowski Distance and Data Standardization

“…In [30] the reverse time series, obtained by multiplying original time series by -1, have been also considered. But to the best of our knowledge the properties of time series shape association measures have been systematically studied only in the pioneering work [9], see also [5].…”

“…An influence of standardization methods on results of cluster analysis has been studied in several works [18,19,[25][26][27] but sometimes the conclusions of such analysis are contradictory. Description and applications of local trend association measures based on moving approximation transform can be found in [6,3,5]. In comparison with similarity measures the association measures give more powerful instrument for analysis of possible relationships between time series.…”

“…is usually based on simulation and modeling of system dynamics but often such modeling is cost prohibitive or cannot give adequate results due to systems complexity or absence of information necessary for models. In such cases a data driven approach to analysis of complex systems including analysis of relationships between dynamics of system elements can be helpful and complementary to conventional modeling [3,5,6,8,17,21,22].…”

“…The correlation coefficient is used for measuring possible direct and inverse relationships between variables. It is considered as a measure of the strength of linear relationship between variables but it is not relevant for measuring possible associations between variables in general case [4] and for measuring associations between time series shapes [5].…”

“…, that is similar to Person's correlation coefficient but uses another central measure. In [5], it was shown that the correlation coefficient is not relevant for measuring shape association of time series. So, before applying a constructed shape association measure on real tasks it is desirable to test its efficiency on testing examples.…”