Selecting time-series hyperparameters with the artificial jackknife

A generalisation of the delete- d jackknife is proposed for solving hyperparameter selection problems in time series. The method is referred to as the artificial delete- d jackknife, emphasizing that it replaces the classic removal step with a fictitious deletion, wherein observed data points are replaced with artificial missing values. This procedure preserves the data order, ensuring seamless compatibility with time series. The approach is asymptotically justified and its finite-sample properties are studied via simulations. In addition, an application based on foreign exchange rates illustrates its practical relevance.