arXiv 11 Jun 2025 · Econometrics
arXiv:2506.09575 · PDF · DOI · OpenAlex · Extracted main text
We study the accuracy of forecasts in the diffusion index forecast model with possibly weak loadings. The default option to construct forecasts is to estimate the factors through principal component analysis (PCA) on the available predictor matrix, and use the estimated factors to forecast the outcome variable. Alternatively, we can directly relate the outcome variable to the predictors through either ridge regression or random projections. We establish that forecasts based on PCA, ridge regression and random projections are consistent for the conditional mean under the same assumptions on the strength of the loadings. However, under weaker loadings the convergence rate is lower for ridge and random projections if the time dimension is small relative to the cross-section dimension. We assess the relevance of these findings in an empirical setting by comparing relative forecast accuracy for monthly macroeconomic and financial variables using different window sizes. The findings support the theoretical results, and at the same time show that regularization-based procedures may be more robust in settings not covered by the developed theory.
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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 | Boot, T. and Nibbering, D (2019) Forecasting using random subspace methods self | 1.000 | 7 | 3 | 100% |
| 2 | De Mol, C., Giannone, D., and Reichlin, L (2008) Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components? | 1.000 | 5 | 3 | 100% |
| 3 | Stock, J. H. and Watson, M. W (2002) Forecasting using principal components from a large number of predictors | 1.000 | 5 | 3 | 100% |
| 4 | Bai, J. and Ng, S (2023) Approximate factor models with weaker loadings | 0.780 | 19 | 5 | 47% |
| 5 | McCracken, M. W. and Ng, S (2016) FRED-MD: A monthly database for macroeconomic research | 0.737 | 3 | 2 | 100% |
| 6 | McCracken, M. and Ng, S (2020) FRED-QD: A quarterly database for macroeconomic research | 0.737 | 3 | 2 | 100% |
| 7 | Bai, J. and Ng, S (2006) Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions | 0.644 | 2 | 2 | 100% |
| 8 | Ahn, S. C. and Horenstein, A. R (2013) Eigenvalue ratio test for the number of factors | 0.511 | 2 | 2 | 50% |
| 9 | Fan, J. and Liao, Y (2022) Learning latent factors from diversified projections and its applications to over-estimated and weak factors | 0.511 | 2 | 1 | 100% |
| 10 | Onatski, A (2012) Asymptotics of the principal components estimator of large factor models with weakly influential factors | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 30 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings | 0.511 | 2 | 1 |