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High-dimensional penalized ARCH processes. (English) Zbl 1490.62264

Summary: We introduce a general methodology to consistently estimate multidimensional ARCH models equation-by-equation, possibly with a very large number of parameters through penalization (Sparse Group Lasso). Some families of multidimensional ARCH models are proposed to tackle homogeneous or heterogeneous portfolios of assets. The corresponding conditions of stationarity and of positive definiteness are studied. We evaluate the relevance of such a strategy by simulation. The relative forecasting performances of our models are compared through the management of financial portfolios.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62J07 Ridge regression; shrinkage estimators (Lasso)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G10 Portfolio theory

Software:

glasso
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References:

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