Semiparametric Approaches to Signal Extraction Problems in Economic Time Series: The Case of the Spanish Industrial Production Index.

Resumen

The Spanish industrial production index, like similar indexes for other countries, contains a mixture of trend, seasonal and irregular components. In time-series analysis generally, nonparametric regression has been very useful for extracting trends, but this approach performs poorly when seasonality is present. To overcome this difficulty, particularly for the Spanish index, we propose two new models for the seasonal effects. The first is a dummy-variable specification; the resulting combined model for the seasonal and trend components is a 'partial linear model'. The second takes seasonality as a smooth function of time; a 'generalized additive model' is obtained. We offer efficient algorithms for calculating values of the parameter-estimators for each of these approaches, and we derive asymptotic properties of these estimators. We show that the estimators for both new approaches perform well when estimating the trend within the Spanish index. Of the two new modelling approaches, the first can be viewed as a special case of the second.