2022 Fiscal Year Research-status Report
Sparse statistical approach for multivariate modelling
| Project/Area Number |
22K13377
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Keywords | Asymptotic theory / Copulas / Factor models / Sparsity / Time series |
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| Outline of Annual Research Achievements |
The research focused on the sparse modelling of multivariate models and the development of parsimonious statistical methods. The sparse modelling aimed to improve the prediction accuracy and the precision of the estimators. The main part of the research was devoted to the derivation of the theoretical properties of such sparse techniques (mainly large sample analysis) and to the assessment of the empirical performances of illustrate the relevance of the sparse modelling. We could develop fast solving algorithms and showed that the sparse approach provides good theoretical properties. We could model high-dimensional random vectors and fix the curse of dimensionality.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The research is having a good progress: one paper on the sparse modelling and identification of Structural Vector Autoregression has been published.
One paper on the sparse modelling of copulas is currently revised and resubmitted.
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| Strategy for Future Research Activity |
We will apply the sparse modelling to two multivariate models: copulas within the semi-parametric setting; factor models, where the penalization will be applied to the factor loading matrix. We will derive the conditions for the oracle property (for both fixed and diverging dimension cases) and apply the method to financial data (portfolio allocation). We expect the following issues:
- for copulas: the non-parametric transformation on the marginal distributions will be the most difficult problem; the theoretical properties will significantly depend on this transformation.
- for factor models: the treatment of the rotational indeterminacy while fostering sparsity will be the most difficult task.
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| Causes of Carryover |
The article "Mac Computer", necessary to perform empirical applications for the proposed research, did not require the full expected amount.
The remaining amount will be used for the purchase of a "Dell Tower Computer": in light of the research applications, the simulated and real data experiments require computers equipped with suitable properties (in terms of GhZ, memory, etc).
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