Approximate Factor Model with S-vine Copula Structure

TL;DR

This paper introduces a new approximate factor model that uses an S-vine copula to better capture complex dependencies among factors, combining PCA and maximum likelihood estimation for improved modeling.

Contribution

It develops a novel two-step estimation method integrating S-vine copulas with factor analysis, providing theoretical guarantees and practical applications in financial risk forecasting.

Findings

Consistent estimation of rotation and copula parameters.

Demonstrated convergence in simulations with increasing dimensions.

Effective VaR forecasting for S&P 500 index using the proposed model.

Abstract

We propose a novel framework for approximate factor models that integrates an S-vine copula structure to capture complex dependencies among common factors. Our estimation procedure proceeds in two steps: first, we apply principal component analysis (PCA) to extract the factors; second, we employ maximum likelihood estimation that combines kernel density estimation for the margins with an S-vine copula to model the dependence structure. Jointly fitting the S-vine copula with the margins yields an oblique factor rotation without resorting to ad hoc restrictions or traditional projection pursuit methods. Our theoretical contributions include establishing the consistency of the rotation and copula parameter estimators, developing asymptotic theory for the factor-projected empirical process under dependent data, and proving the uniform consistency of the projected entropy estimators. Simulation studies demonstrate convergence with respect to both the dimensionality and the sample size. We further assess model performance through Value-at-Risk (VaR) estimation via Monte Carlo methods and apply our methodology to the daily returns of S&P 500 Index constituents to forecast the VaR of S&P 500 index.