Semiparametric approaches to signal extraction problems in economic time series

摘要

Nonparametric regression methods have become a very useful tool to extract trend signals in economic time series. However, this approach performs poorly when seasonality is present. To overcome this difficulty, we propose two alternative methods to deal with seasonal effects. In both approaches the trend is specified nonparametrically, but the seasonal component specification is different. First, we propose a partial linear model where the parametric part is a dummy-variable specification for the seasonality. Secondly, we consider the seasonal component to be a smooth function of time and, therefore, the model falls within the class of additive models. We offer efficient algorithms for calculating values of the parameter estimators for each of these approaches and we derive asymptotic properties for the estimators in the partial linear model. Finally, we illustrate these methods when applied to the Spanish industrial production index for energy.