arXiv 27 Jul 2021 · Econometrics
arXiv:2107.12552 · PDF · DOI · OpenAlex · Extracted main text
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or exceeds the sample size, we adopt a sparse framework and propose two penalized maximum likelihood estimators with either the Lasso or the smoothly clipped absolute deviation (SCAD) penalty. We show that both estimators are estimation consistent, while the SCAD estimator also selects relevant parameters with probability approaching one. A modified EM-algorithm is developed for the case of Gaussian errors and simulations show that the algorithm exhibits desirable finite sample performance. In an application to short-horizon return predictability in the US, we estimate a 15 variable 2-state MS-VAR(1) and obtain the often reported counter-cyclicality in predictability. The variable selection property of our estimators helps to identify predictors that contribute strongly to predictability during economic contractions but are otherwise irrelevant in expansions. Furthermore, out-of-sample analyses indicate that large MS-VARs can significantly outperform "hard-to-beat" predictors like the historical average.
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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 | Callot, L., Kock, A.B (2015) Oracle inequalities for high dimensional vector autoregressions | 1.000 | 5 | 3 | 100% |
| 2 | Goyal, A., Welch, I (2008) A comprehensive look at the empirical performance of equity premium prediction | 0.874 | 5 | 2 | 100% |
| 3 | Fan, J., Xue, L., Zou, H (2014) Strong oracle optimality of folded concave penalized estimation | 0.811 | 4 | 2 | 100% |
| 4 | Kwon, S., Kim, Y (2012) Large sample properties of the scad-penalized maximum likelihood estimation on high dimensions | 0.737 | 4 | 2 | 75% |
| 5 | Henkel, S.J., Martin, J.S., Nardari, F (2011) Time-varying short-horizon predictability | 0.737 | 3 | 2 | 100% |
| 6 | Li, D., Ke, Y., Zhang, W (2015) Model selection and structure specification in ultra-high dimensional generalised semi-varying coefficient models | 0.737 | 3 | 2 | 100% |
| 7 | Friedman, J., Hastie, T., Tibshirani, R (2008) Sparse inverse covariance estimation with the graphical lasso | 0.644 | 2 | 2 | 100% |
| 8 | Zhao, P., Yu, B (2006) On model selection consistency of lasso | 0.644 | 2 | 2 | 100% |
| 9 | Zhu, X (2020) Nonconcave penalized estimation in sparse vector autoregression model | 0.644 | 2 | 2 | 100% |
| 10 | Zou, H., Li, R (2008) One-step sparse estimates in nonconcave penalized likelihood models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 53 scored citations.