Shrinkage Estimation of Semiparametric Multiplicative Error Models

Abstract

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data and the recently proposed Focused Information Criterion. We illustrate such a methodology using a simple semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that from a forecasting perspective such a procedure outperforms other estimation procedures.