Simulation Structure for Selecting an Optimal Error Distribution Through the GAS Model

Abstract

In econometrics and finance, volatility modelling has long been a specialised field for addressing a variety of issues that pertain to the risks and uncertainties of an asset. However, volatility modelling for risk management is highly dependent on the underlying error distribution. Hence, this study presents a Monte Carlo simulation (MCS) structure for selecting an optimal or the most adequate error distribution that is relevant for modelling the persistence of volatility through the Generalized Autoregressive Score (GAS) model. The structure describes an organised approach to the MCS experiment that includes “background of the study (optional), defining the aim of the study, specifying the research questions, method of implementation, and summarised conclusion”. The method of implementation is a process that consists of writing the simulation code, setting the seed, setting the true parameter a priori, data generation, and performance evaluation throughmeta-statistics. Among the findings, the study used both fat-tails and √N consistency experiments to show that the GAS model with a lower unconditional shape parameter value (ˆν∗ = 4.1) can generate a dataset that adequately reflects the behaviour of financial time series data, relevant for volatility modelling. This dynamic structure is intended to help interested users on MCS experiments utilising the GAS model for reliable volatility persistence calculations in finance and other areas.