Applying spline-based phase analysis to macroeconomic dynamics

Abstract The article uses spline-based phase analysis to study the dynamics of a time series low-frequency data on values certain economic indicator. approach includes two stages. At first stage, original is approximated by smooth twice-differentiable function. Natural cubic splines are used as an approximating function y y . Such have smallest curvature over observation interval compared other possible functions that satisfy choice criterion. second trajectory constructed in ( t , ′ ) \left(t,y,y^{\prime} ) -space, corresponding series, and shadow projection onto (y,y^{\prime} -plane. applied GDP indicators for G7 countries. interrelation between loops cycles evolution shown. also discusses features, limitations prospects use analysis.