Linesseries

Linesseries is a term used in data visualization and time-series analysis to describe a sequence of linear representations that collectively approximate a data series. The concept emphasizes piecewise linear structure, where each segment is derived from a linear fit over a specified window or subinterval. The name combines "line" and "series" to reflect its dual nature as both a set of straight-line approximations and a temporally ordered series of fits.

In practice, a linesseries is produced by applying a linear regression to successive subsets of data, typically using a sliding window. For each position t, a straight line is fit to the observations within the window, yielding a segment defined by its slope and intercept. The collection of segments forms a polyline that follows the trajectory of the original series. Variants may use weighted fits, robust regression, or adaptive window lengths to emphasize different scales of variation.

As a representation, a linesseries highlights local trends and discontinuities while omitting some nonlinearity between segment endpoints. It provides a multi-scale view when multiple window sizes are used, enabling analysts to compare short-term fluctuations against longer-term tendencies. The mathematical relationship between consecutive segments can be analyzed to detect regime shifts or structural breaks.

Applications include financial data visualization, signal processing, and exploratory data analysis, where a simple, interpretable summary of complex behavior is desired. Limitations include sensitivity to window length, potential edge effects, and the risk of over-smoothing. Related concepts include piecewise linear modeling, moving averages, and local regression (LOESS).