Trend Analysis of Fragmented Time Series: Hypothesis Testing Based Adaptive Spline Filtering Method

Missing data present significant challenges to trend analysis of time series. Straightforward approaches consisting of supplementing missing data with constant or zero values or with linear trends can severely degrade the quality of the trend analysis, which significantly reduces the reliability of the trend analysis. We present a robust adaptive approach to discover the trends from fragmented time series. The approach proposed in this paper is based on the HASF (Hypothesis-testing-based Adaptive Spline Filtering) trend analysis algorithm, which can accommodate non-uniform sampling and is therefore inherently robust to missing data. HASF adapts the nodes of the spline based on hypothesis testing and variance minimization, which adds to its robustness.