Parsimonious statistical modelling for high-dimensional problems
| Project/Area Number |
19K23193
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
0107:Economics, business administration, and related fields
|
|---|
| Research Institution | Osaka University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2019-08-30 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2022)
|
| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | Copulas / Factor models / Financial econometrics / Sparsity / Asymptotic theory / Time series / High-dimensions / M-estimation / High dimension / High-dimension / Multivariate Time Series / Penalisation |
|---|
| Outline of Research at the Start |
The proposed research would be dedicated to high-dimensional variance covariance models. Within the family of stochastic volatility processes, we would consider a penalised M-estimation criterion to estimate such models. New penalty functions able to capture breaks among time series will be studied. This modelling would be justified by theoretical results and its relevance assessed based on simulated data and real portfolios.
Furthermore, a general penalised framework will be considered to provide finite sample properties of sparse M-estimators and applied to a broad range of models.
|
| Outline of Final Research Achievements |
The research was devoted to the sparse modelling of multivariate models and to the development of statistical methods to fix the curse of dimensionality. The sparse approach aimed to improve the precision of the M-estimators and to improve the prediction performances. Three multivariate models were under consideration: multivariate stochastic volatility models (financial econometrics literature); factor models; copula models. For each of these models, we specified a sparsity-based estimation framework, derived the corresponding theoretical properties (finite/large sample properties) and illustrated the relevance of the proposed method through numerical experiments. In particular, the specification of a suitable M-estimation criterion was key to allow for fast-solving implementation methods. We could apply the sparse modelling to high-dimensional random vectors (e.g., financial data) and obtain better out-of-sample performances compared to non-sparse methods.
|
| Academic Significance and Societal Importance of the Research Achievements |
The curse of dimensionality is the main drawback inherent to most multivariate models due to the explosive number of parameters. The research main purpose was to fix this curse, provide methods to efficiently model high-dimensional vectors and improve the prediction performances.
|
Report
(5 results)
Research Products
(31 results)
