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Sparse Bayesian time-varying covariance estimation in many dimensions. (English) Zbl 1452.62773

Summary: We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors towards zero. To demonstrate the merits of the proposed framework, the model is applied to simulated data as well as to daily log-returns of 300 S&P 500 members. Our approach yields precise correlation estimates, strong implied minimum variance portfolio performance and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91G10 Portfolio theory
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