Abstract
This article studies the estimation of the constrained factor models for high-dimensional time series. The approach is based on the eigenanalysis of a non-negative definite matrix constructed from the auto-covariance matrices. The convergence rate of the estimator for loading matrix and the asymptotic normality of the estimated factor score are explored under regularity conditions set for the proposed model. Our estimation for the constrained factor models can achieve the optimal rate of convergence even in the case of weak factors. The finite sample performance of our approach is examined and compared with the existing methods by Monte Carlo simulations. Our methodology is illustrated and supported by a real data example.
| Original language | English |
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| Number of pages | 26 |
| Journal | Journal of Forecasting |
| Early online date | 5 Jan 2025 |
| DOIs | |
| Publication status | E-pub ahead of print - 5 Jan 2025 |
Funding
The authors thank the editor-in-chief and the anonymous reviewers for their comments that significantly improved this work. The research of Qiang Xia was supported in part by the National Natural Science Foundation of China (No.12171161, 91746102) and the Natural Science Foundation of Guangdong Province of China (No.2022A1515011754).
Keywords
- constrained factor models
- high-dimensional time series
- convergence rate
- asymptotic normality