Simulation Framework to Determine Suitable Innovations for Volatility Persistence Estimation: The GARCH Approach

Abstract

This study rolls out a robust framework relevant for simulation studies through the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model using the rugarch package. The package is thoroughly investigated, and novel findings are identified for improved and effective simulations. The focus of the study is to provide necessary simulation steps to determine appropriate distributions of innovations relevant for estimating the persistence of volatility. The simulation steps involve “background (optional), defining the aim, research questions, method of implementation, and summarised conclusion”. The method of implementation is a workflow that includes writing the code, setting the seed, setting the true parameters a priori, data generation process and performance assessment through meta-statistics. These novel, easy-to-understand steps are demonstrated on financial returns using illustrative Monte Carlo simulation with empirical verification. Among the findings, the study shows that regardless of the arrangement of the seed values, the efficiency and consistency of an estimator generally remain the same as the sample size increases. The study also derived a new and flexible true-parameter-recovery measure which can be used by researchers to determine the level of recovery of the true parameter by the MCS estimator. It is anticipated that the outcomes of this study will be broadly applicable in finance, with intuitive appeal in other areas, for volatility modelling.