TY - JOUR
T1 - New HEAVY Models for Fat-Tailed Realized Covariances and Returns
AU - Opschoor, Anne
AU - Janus, Pawel
AU - Lucas, André
AU - Van Dijk, Dick
PY - 2018/10/2
Y1 - 2018/10/2
N2 - We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.
AB - We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.
KW - Generalized autoregressive score (GAS) dynamics
KW - Heavy tails
KW - Matrix-F distribution
KW - Multivariate volatility
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U2 - 10.1080/07350015.2016.1245622
DO - 10.1080/07350015.2016.1245622
M3 - Article
AN - SCOPUS:85019218639
SN - 0735-0015
VL - 36
SP - 643
EP - 657
JO - Journal of Business & Economic Statistics
JF - Journal of Business & Economic Statistics
IS - 4
M1 - 36
ER -