Flexible Time Series Forecasting Using Shrinkage Techniques and Focused Selection Criteria

Nonlinear time series models can exhibit components such as long range trends and seasonalities that may be modeled in a flexible fashion. The resulting unconstrained maximum likelihood estimator can be too heavily parameterized and suboptimal for forecasting purposes. The paper proposes the use of a class of shrinkage estimators that includes the Ridge estimator for forecasting time series, with a special attention to GARCH and ACD models. The local large sample properties of this class of shrinkage estimators is investigated. Moreover, we propose symmetric and asymmetric focused selection criteria of shrinkage estimators. The focused information criterion selection strategy consists of picking up the shrinkage estimator that minimizes the estimated risk (e.g. MSE) of a given smooth function of the parameters of interest to the forecaster. The usefulness of such shrinkage techniques is illustrated by means of a simulation exercise and an intra-daily financial durations forecasting application. The empirical application shows that an appropriate shrinkage forecasting methodology can significantly outperform the unconstrained ML forecasts of rich flexible specifications.