Dr. Chao Zhang

We introduce a novel method to forecast the realised covariances of multidimensional time series. The central innovation of our method is a two-step procedure which first filters the training data by relevance before using non-parametric or linear approaches to make predictions. The relevance filter uses the recent histories of both the test input and each individual training input to generate a pairwise measure of dissimilarity between the two points. Highly dissimilar training data which do not share the observed dynamics of the test input are discarded from the regression procedure, reducing the complexity of the forecasting task. The second step uses simple non-parametric or linear methods to perform regression with the relevant data from the first step. Our method produces fast, interpretable predictions which achieve state-of-the-art performance, and functions well in limited-data availability and high dimensional settings such as large covariance matrices because it does not depend on highly parameterised models. Furthermore, we propose a dynamic ensembling scheme to combine our method with existing models. The scheme uses information about the recent performance of forecasts from different models to produce a weighted average forecast which heavily discounts models ill-suited to the current market dynamics. We test our methods on realised covariance data of U.S. equities and find significant improvements over widely used benchmarks.