# Inverse Moment Methods for Sufficient Forecasting using High-Dimensional Predictors

arXiv: https://arxiv.org/abs/1705.00395 · HTML: https://mlsanity.com/paper/1705.00395/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2017.

## Built on by (most cited first, 9 of 9)

- [Dimension Reduction for Fr'echet Regression](https://mlsanity.com/paper/2110.00467/) (2021)
- [Nonlinear Sufficient Dimension Reduction for Distribution-on-Distribution Regression](https://mlsanity.com/paper/2207.04613/) (2022)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models](https://mlsanity.com/paper/2505.20536/) (2025)
- [Supervised Dynamic Dimension Reduction with Deep Neural Network](https://mlsanity.com/paper/2508.03546/) (2025)
- [Factor Augmented Supervised Learning with Text Embeddings](https://mlsanity.com/paper/2508.06548/) (2025)
- [Mining the Factor Zoo: Estimation of Latent Factor Models with Sufficient Proxies](https://mlsanity.com/paper/2212.12845/) (2022)
- [Structure-Preserving Nonlinear Sufficient Dimension Reduction for Tensors](https://mlsanity.com/paper/2512.20057/) (2025)
- [Factor Augmented High-Dimensional SGD](https://mlsanity.com/paper/2605.19291/) (2026)

## Abstract (arXiv)

We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors, to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of sufficient dimension reduction, the proposed methods can capture the non-monotone effect of factors on the response. We also allow a diverging number of factors and only impose general regularity conditions on the distribution of factors, avoiding the undesired time reversibility of the factors by the latter. These make the proposed methods fundamentally more applicable than the sufficient forecasting method in Fan et al. (2017). The proposed methods are demonstrated in both simulation studies and an empirical study of forecasting monthly macroeconomic data from 1959 to 2016. Also, our theory contributes to the literature of sufficient dimension reduction, as it includes an invariance result, a path to perform sufficient dimension reduction under the high-dimensional setting without assuming sparsity, and the corresponding order-determination procedure.