$$\ell _{1}$$ Common Trend Filtering

Abstract The $$\ell _{1}$$ ℓ 1 trend filtering enables us to estimate a continuous piecewise linear of univariate time series. This filter and its variants have subsequently been applied in various fields, including astronomy, climatology, economics, electronics, environmental science, finance, geophysics. Although the can series, it cannot common multiple paper develops statistical procedure that it, which is multivariate extension filtering. We provide an algorithm for estimating clue specify tuning parameter procedure, both required application. also (i) numerically illustrate how well works, (ii) empirical illustration, (iii) introduce generalization our novel method.