Mixed data sampling regression: Parameter selection of smoothed least squares estimator

Abstract

AbstractWe investigate mixed data sampling (MIDAS) regression models, which include time series data sampled at different frequencies. MIDAS framework introduced by Ghysels et al. (2004, 2005, 2006, 2007) comprises diverse lag structures that are employed for parameterizing the regression model. Since some specific parametric functions are utilized, MIDAS is a parametric approach and thus nonlinear least squares (NLS) technique is used to estimate the parameters. In this parametric approach, the shape of the lag distribution is controlled by an arbitrary class of parametric functions, but unfortunately, inaccurate approximations of the lag distribution may arise under such a circumstance. Breitung and Roling (2015) suggested a nonparametric approach as a solution to this complication. The product of this approach is smoothed least squares (SLS) estimator which depends on a smoothing parameter. The main objective of this paper is to solve the complexity of selecting this parameter. We offer various selection methods for the smoothing parameter to enhance the performance of the SLS estimator. A Monte Carlo simulation is conducted to test the effect of different choices of the smoothing parameter on the performance of the SLS estimator by means of both in‐sample and out‐of‐sample forecasting. Additionally, we carry out a data analysis where future values of gross domestic product are forecasted by unemployment rate.