Higher Moment Constraints for Predictive Density Combinations
30 Pages Posted: 16 Jan 2019
Date Written: November 22, 2018
Abstract
The majority of nancial data exhibit asymmetry and heavy tails, which makes forecasting the entire density critically important. Recently, a forecast combination methodology has been developed to combine predictive densities. We show that combining individual predictive densities that are skewed and/or heavy-tailed results in significantly reduced skewness and kurtosis. We propose a solution to overcome this problem by deriving optimal log score weights under Higher-order Moment Constraints (HMC). The statistical properties of these weights are investigated theoretically and through a simulation study. Consistency and asymptotic distribution results for the optimal log score weights with and without high moment constraints are derived. An empirical application that uses the S&P 500 daily index returns illustrates that the proposed HMC weight density combinations perform very well relative to other combination methods.
Keywords: Forecast Combination, Predictive Densities, Optimal Weights, Skewness, Kurtosis
JEL Classification: C53, C58
Suggested Citation: Suggested Citation