Index Tracking via Temporally Weighted Least Squares and Gaussian Process Regressions

As a primary passive investment strategy, index tracking replicates the performance of a specific financial market index by minimizing tracking errors. Most existing index tracking methods are developed based on the assumption that all historical data are equally important. As a result, the importance of different historical data may be overlooked. This article addresses index tracking via temporally weighted least-squares regression. The weight for each time period except for the latest one is defined as the reciprocal of the largest absolute residual of the returns between the index currently and all the selected stocks in the subsequent periods. The weight for the latest period is inferred from the weights in the preceding periods via Gaussian process regression. The tracking accuracy and consistency of the proposed approach are demonstrated via experimentation on historical data from seven major stock markets.