  It is surprising that last two decades many works in time series data mining
and clustering were concerned with measures of similarity of time series but
not with measures of association that can be used for measuring possible direct
and inverse relationships between time series. Inverse relationships can exist
between dynamics of prices and sell volumes, between growth patterns of
competitive companies, between well production data in oilfields, between wind
velocity and air pollution concentration etc. The paper develops a theoretical
basis for analysis and construction of time series shape association measures.
Starting from the axioms of time series shape association measures it studies
the methods of construction of measures satisfying these axioms. Several
general methods of construction of such measures suitable for measuring time
series shape similarity and shape association are proposed. Time series shape
association measures based on Minkowski distance and data standardization
methods are considered. The cosine similarity and the Pearsons correlation
coefficient are obtained as particular cases of the proposed general methods
that can be used also for construction of new association measures in data
analysis.
