Adaptive LASSO for selecting Fourier coefficients in a functional smooth time-varying cointegrating regression: An application to the Feldstein–Horioka puzzle

This paper proposes a simple routine to select the specification of a time-varying cointegration model based on a combination of polynomials. Whereas information criteria or approaches based on sequential general to specific testing procedures are commonly used for that issue, to our knowledge, there exists no formal proof of the consistency of these selection methods for these models. In addition, these latter strategies imply exhaustive searches which may be computationally cumbersome. We suggest to use a widespread technique in machine learning, a LASSO-based procedure, that sets the right number of polynomials to combine for describing the time-varying dynamic in a cointegrating regression. Monte Carlo experiments show that the selection consistency of the Adaptive LASSO holds in our context. We applied the outlined methodology to the degree of capital mobility for the some European economies and we found a decline of saving retention within the last two decades.