Shrinkage Estimation of Regression Models with Multiple Structural Changes

In this paper we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso (least absolute shrinkage and selection operator ). We show that with probability tending to one our method can correctly determine the unknown number of breaks and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a datadriven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.