Analysis of a long-memory Garch-type model of stock returns and their risk measures

The purpose of this article is to investigate whether considering stylized facts in financial time series leads to better estimation of risk measures. This study focuses on long-memory GARCH-type models chosen for their ability to capture characteristics of financial time series like long memory and volatility clustering. There are periods of high and low volatility in financial markets. One of the most important ways to reduce risk is to use a time-series model to manage market risk. In comparison to long-memory GARCH-type models, such as fractionally integrated generalised autoregressive conditional heteroskedasticity and hyperbolic generalised autoregressive conditional heteroskedasticity, this research study aims to determine how effective the fractionally integrated asymmetric power autoregressive conditional heteroskedasticity is at producing competitive risk measures. The stock returns are assumed to follow a family of extreme parametric distributions in long-memory GARCH-type models. The historical closing price time series for both short and long trading positions on the various confidence levels correspond to the left and right quantiles of the return distributions, respectively. The findings show that FIAPARCH with Student's-t distribution has a high chance of becoming a suitable model for generating reliable risk measures. However, FIGARCH fits the data well to generate risk measures when using the presumptive skewed Student's-t distribution model.