Inverse moment methods for sufficient forecasting using high-dimensional predictors

Eigenvalue ratio test for the number of factors

Wei Luo, Lingzhou Xue, Jiawei Yao and Xiufan Yu

Biometrika, 2022, vol. 109, issue 2, 473-487

Abstract: SummaryWe 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 nonmonotone 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 of Fan et al. (2017). The proposed methods are demonstrated both in 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.

Keywords: Factor model; Forecasting; High-dimensional asymptotics; Invariance property; Principal component; Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asab037 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:109:y:2022:i:2:p:473-487.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().