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Copula-Based Vector Autoregressive Modeling for Volatility Index Data
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DOI：10.1007/s42519-025-00524-5.png)
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Abstract
En 中文
Time series are ubiquitous in finance, where they are often reported daily with opening and closing observations. Daily opening and closing values for the popular stock market volatility index (VIX) are widely considered to inform investment decisions. Traditional time series techniques, such as the vector autoregressive (VAR) model, are widely used to analyze multiple interrelated time series and should be adopted and extended to analyze such data. However, VAR models typically assume multivariate normal error distributions, which may limit their applicability to such data with complex dependency structures and heavy-tailed marginal distributions. This study aims to propose a copula-based VAR-VIX model and discuss the extension of the classical VAR model for analyzing the VIX from 2006 to 2022. This is done by incorporating flexible marginal error distributions and copula-based frameworks to capture the intricate dependencies between the correlated opening and closing values, thus providing a more robust and flexible modeling approach. This copula-based VAR-VIX model compares forty-three fitted models, including the classical VAR model, six standard-copula VAR models, and fifteen mixture-copula VAR models, each with normal and t-marginal distributions. Model selection is conducted, and results show that the VAR-VIX model with a Gaussian-Frank mixture-copula and t-marginal error distribution best fits the VIX data.
Keywords:
Multivariate time series
Vector autoregressive model
Copula and mixture-copula
Volatility index data
Maximum likelihood estimation
Journal
J
IF:
0.9
Papers:
85
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0