A High-Frequency Semiparametric Dynamic Functional Arma-Garch-Copula Approach For Risk Forecasting

Abstract

This paper introduces a novel Semiparametric Dynamic Functional (SDF) ARMA-GARCH-Copula framework to forecast daily financial risk measures from high- frequency intradaily data. Our proposed methodology is capable of dealing with high-dimensional financial time series. It blends together a high-frequency ARMA-GARCH-Copula structure and a flexible dynamic nonparametric functional representation of the innovation distributions. We approach probability density functions (PDFs) of standardized intradaily GARCH residuals (obtained via quasi-maximum likelihood – QML) as time-varying curve time series and employ functional factor models (FFM), with and without sparsity and dynamic sparsity, and dynamic functional principal components (DFPC) to capture the PDFs dynamics, reduce dimensionality in a two-way perspective and forecast the PDFs curves themselves. By combining the estimated ARMA-GARCH-Copula structure with the forecasted PDFs curves, we simulate future intradaily returns and derive predictions for daily volatility, Value-at-Risk (VaR), and Expected Shortfall (ES). We conduct an empirical analysis on 5-minute returns of 22 cryptocurrencies from January 2022 to July 2023. The results suggest that our proposed SDF ARMA-GARCH-Copula variations outperform a daily GARCH benchmark in volatility forecasting and provide well-behaved risk estimated, highlighting the value of incorporating dynamic flexible error PDFs for daily risk forecasting. Joint work with Klaus Boesch, Jean-David Fermanian and Hugo Inzirillo.

Short bio

Flavio A. Ziegelmann is a Full Professor of Statistics and Econometrics in the Department of Statistics at the Universidade Federal do Rio Grande do Sul (UFRGS), Brazil, and currently serves as President of the Brazilian Statistical Association. His research interests include nonlinear, high-dimensional, and functional time series, dynamic copulas, regularisation methods, financial econometrics, frontier estimation, and machine learning for forecasting and casual analysis, with applications in finance and economics. He has published a blend of theoretical and applied papers in journals such as Econometric Theory, Annals of Statistics, Insurance: Mathematics and Economics, Quantitative Finance, International Journal of Forecasting, Stochastic Processes and their Applications, Econometrics Reviews, among others. He serves as Associate Editor for EconomicA and PlosOne.