  This paper introduces a multiscale analysis based on optimal piecewise linear
approximations of time series. An optimality criterion is formulated and on its
base a computationally effective algorithm is constructed for decomposition of
a time series into a hierarchy of trends (local linear approximations) at
different scales. The top of the hierarchy is the global linear approximation
over the whole observational interval, the bottom is the original time series.
Each internal level of the hierarchy corresponds to a piecewise linear
approximation of analyzed series. Possible applications of the introduced
Multiscale Trend Analysis (MTA) go far beyond the linear interpolation problem:
This paper develops and illustrates methods of self-affine, hierarchical, and
correlation analyses of time series.
