Trend filtering by adaptive piecewise polynomials

Trend filtering is a regression problem to estimate underlying trends in time series data. It is necessary to investigate data in various disciplines. We propose a trend filtering method by adaptive piecewise polynomials. More specifically, we adjust the location and the number of breakpoints or knots to obtain a better fitting to given data. The numerical results on synthetic and real data sets show that it captures distinct features such as abrupt changes or kinks and provides a simplified form and brief summary of given data. •A trend filtering method by adaptive piecewise polynomials is proposed.•The proposed method adjusts the location and the number of breakpoints to obtain a better fitting to given data.•The proposed method captures distinct features such as abrupt changes or kinks and provides a simplified form and brief summary of given data.