Financial Statistical Modelling With a New Nature-Inspired Technique

This paper introduces a nature-inspired intelligent model suitable for high-frequency financial time series. It combines a neural network parametrization for the mean with a linear (GARCH) parametrization for the variance. We propose a complete model-building cycle for the family of NN-GARCH specifications that includes all three stages of econometric modelling (specification, estimation and evaluation). Based on the maximum likelihood theory, we device procedures for statistical inference in the framework of NN-GARCH models and thus offer the modeler the opportunity to test hypotheses of interest concerning both the mean and variance structure of the data-generating process. We demonstrate the model-building cycle by constructing a NN-GARCH dynamic model for the returns on the DAX Stock Index