Nonnegative group bridge and application in financial index tracking

The stock index plays an increasingly important role in investors’ decision-making. With the continuous development of the stock markets and the advancement of financial technology, the methods of compiling stock indices have consistently improved. Index tracking attempts to match the performance of a target market index by setting up a portfolio of assets to obtain similar returns to the target index. Therefore, the methods of selecting which stocks constitute a portfolio are very important. In daily investing, investors select quality assets from the target index to include in their tracking portfolio. In this paper, a nonnegative group bridge method is proposed for variable selection and estimation of grouping variables without overlapping to aid stock selection. The estimation consistency, variable-selection consistency, and asymptotic property of this method are provided. To obtain the solution of this model, we use an idea based on the local group coordinate descent method. Using tracking error as the criterion, the nonnegative group bridge estimation method is found superior to other nonnegative methods in terms of goodness-of-fit.