arXiv 3 Jul 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2307.01033 · PDF · DOI · OpenAlex · Extracted main text
We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a transformation of the dependent variable and a pre-estimated tail quantile. Leveraging a sparsity condition, we derive a nonasymptotic bound on the prediction and estimator errors of the ES estimator, accounting for the estimation error in the dependent variable, and provide conditions under which the estimator is consistent. Our estimator is applicable to heavy-tailed time-series data and we find that the amount of parameters in the model may grow with the sample size at a rate that depends on the dependence and heavy-tailedness in the data. In an empirical application, we consider the systemic risk measure CoES and consider a set of regressors that consists of nonlinear transformations of a set of state variables. We find that the nonlinear model outperforms an unpenalized and untransformed benchmark considerably.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Adrian, T. and Brunnermeier, M. K (2016) CoVaR | 0.874 | 6 | 2 | 100% |
| 2 | Belloni, A. and Chernozhukov, V (2011) $$1-Penalized Quantile Regression in High-Dimensional Sparse Models | 0.737 | 3 | 3 | 67% |
| 3 | Wong, K. C., Li, Z., and Tewari, A (2020) Lasso Guarantees for $$-Mixing Heavy-Tailed Time Series | 0.737 | 3 | 2 | 100% |
| 4 | Barendse, S (2020) Efficiently Weighted Estimation of Tail and Interquantile Expectations self | 0.737 | 3 | 2 | 100% |
| 5 | Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D (1999) Coherent Measures of Risk | 0.644 | 2 | 2 | 100% |
| 6 | BCBS (2016) Minimum Capital Requirements for Market Risk | 0.644 | 2 | 2 | 100% |
| 7 | Belloni, A., Chen, M., Madrid Padilla, O. H., and Wang, Z (2023) High-Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing | 0.644 | 2 | 2 | 100% |
| 8 | Babii, A., Ghysels, E., and Striaukas, J (2022) Machine Learning Time Series Regressions with an Application to Nowcasting | 0.511 | 2 | 1 | 100% |
| 9 | Christoffersen, P (2011) Elements of Financial Risk Management | 0.511 | 2 | 1 | 100% |
| 10 | Campbell, J. Y. and Hentschel, L (1992) No news is good news: An asymmetric model of changing volatility in stock returns | 0.405 | 1 | 1 | 100% |
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