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Title: Theory and practice of combining forecasts of higher moments in financial data Authors:  Andrey Vasnev - University of Sydney (Australia) [presenting]
Laurent Pauwels - University of Sydney (Australia)
Peter Radchenko - University of Sydney (Australia)
Abstract: The aim is to investigate the theory and practice of two novel approaches to combining forecasts of higher moments, specifically skewness and kurtosis, to predict the moments of implicitly and explicitly combined distributions in financial data. Alternative linear and nonlinear models can be combined to forecast the higher moments using explicitly and implicitly combined models. The first approach combines the models using optimal weights to predict the higher moments of an explicitly combined model. The second approach combines the higher moments of the models using optimal weights to predict the higher moments of an implicitly combined model. We expand the knowledge and techniques of combining forecasts by doubling the number of moments that are considered in the literature from two moments, namely the mean and variance, to four, with the addition of the skewness and kurtosis parameters. Several new versions of the Kullback-Leibler (KL) Information Criterion (IC), or KLIC, also known as the KL divergence or discrimination information, are used to derive the optimal weights for combining forecasts of skewness and kurtosis, and hence to evaluate forecast accuracy of alternative moments. Novel variations and extensions of alternative IC, such as the Akaike IC (AIC), which is an estimator of KLIC, and the Schwartz Bayesian IC (SBIC) and Hannan-Quinn Criterion (HQC), neither of which is an estimator of KLIC, will also be analysed.