Moving Approximation Transform and Local Trend Associations inTime Series Data Bases

The properties of moving approximation (MAP) transform and its application to time series data mining are discussed. MAP transform replaces time series values by slope values of lines approximating time series data in sliding window. A simple method of MAP transform calculation for time series with fixed time step is proposed. Based on MAP the measures of local trend associations and local trend distances are introduced. These measures are invariant under independent linear transformations and normalizations of time series values. Measure of local trend associations defines association function and measure of association between time series. The methods of application of association measure to construction of association network of time series and clustering are proposed and illustrated by examples of economic, financial, and synthetic time series.