arXiv 7 Oct 2019 · Econometrics · publishedJournal of Econometrics (2020) · 6 citations (OpenAlex)
arXiv:1910.03109 · PDF · DOI · OpenAlex · Extracted main text
High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two $L_2$ boosting algorithms for estimating high dimensional models in which the coefficients are modeled as functions evolving smoothly over time and the predictors are locally stationary. The first method uses componentwise local constant estimators as base learner, while the second relies on componentwise local linear estimators. We establish consistency of both methods, and address the practical issues of choosing the bandwidth for the base learners and the number of boosting iterations. In an extensive application to macroeconomic forecasting with many potential predictors, we find that the benefits to modeling time variation are substantial and they increase with the forecast horizon. Furthermore, the timing of the benefits suggests that the Great Moderation is associated with substantial instability in the conditional mean of various economic series.
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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 | Cai, Z (2007) Trending time-varying coefficient time series models with serially correlated errors | 1.000 | 6 | 4 | 100% |
| 2 | Stock, J. H. and Watson, M. W (1996) Evidence on structural instability in macroeconomic time series relations | 1.000 | 5 | 3 | 100% |
| 3 | Robinson, P. M (1989) Nonparametric estimation of time-varying parameters | 0.928 | 4 | 3 | 100% |
| 4 | Dahlhaus, R., Richter, S., and Wu, W. B (2018) Towards a general theory for non-linear locally stationary processes | 0.874 | 9 | 3 | 67% |
| 5 | Lutz, R. W. and Bühlmann, P (2006) Boosting for high-multivariate responses in high-dimensional linear regression | 0.811 | 4 | 2 | 100% |
| 6 | Buhlmann, P (2006) Boosting for high-dimensional linear models | 0.737 | 10 | 5 | 40% |
| 7 | Ding, X., Qiu, Z., Chen, X., et al (2017) Sparse transition matrix estimation for high-dimensional and locally stationary vector autoregressive models | 0.737 | 3 | 2 | 100% |
| 8 | Friedman, J. H (2001) Greedy function approximation: a gradient boosting machine | 0.737 | 3 | 2 | 100% |
| 9 | Stock, J. H. and Watson, M (2009) Forecasting in dynamic factor models subject to structural instability | 0.737 | 3 | 2 | 100% |
| 10 | Wu, W. B (2005) Nonlinear system theory: Another look at dependence | 0.644 | 4 | 2 | 50% |
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