Nonparametric estimation of time varying parameters under shape restrictions

In this paper we propose a new method to estimate nonparametrically a time varying parameter model when some qualitative information from outside data (e.g. seasonality) is available. In this framework we make two main contributions. First, the resulting estimator is shown to belong to the class of generalized ridge estimators and under some conditions its rate of convergence is optimal within its smoothness class. Furthermore, if the outside data information is fullfilled by the underlying model, the estimator shows efficiency gains in small sample sizes. Second, for the implementation process, since the estimation procedure envolves the computation of the inverse of a high order matrix we provide an algorithm that avoids this computation and, also, a data-driven method is derived to select the control parameters. The practical performance of the method is demonstrated in a simulation study and in an application to the demand of soft drinks in Canada.