Journal of Time Series Analysis· 2026Q1
Principal Component Analysis for High‐Dimensional Approximate Factor Models in Time Series: Assumptions, Asymptotic Theory, and Identification
- 3citations
- Q1SCImago
- 2026year
Short summary
Principal Component Analysis (PCA) consistently estimates large approximate factor models in high-dimensional stationary time series panels when both cross-sectional and sample sizes grow infinitely.
AI-generated from the title and abstract; the full text is not read.
Key points
- PCA consistently estimates large approximate factor models in high-dimensional stationary time series panels.
- Consistency and asymptotic normality of PCA estimators are achieved when both cross-sectional and sample sizes grow infinitely.
- Common and idiosyncratic components are identified only in the limit.
- Restrictions are required to uniquely determine factors and loadings, impacting statistical inference.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT We consider estimation of large approximate factor models in high‐dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for consistency and asymptotic normality of the estimators, which hold when both the cross‐sectional dimension and the sample size tend to infinity. Special emphasis is placed on identification. First, we show that the common and idiosyncratic components are identified only in the limit . Second, we discuss the restrictions required to uniquely determine factors and loadings and examine their consequences for statistical inference.
The authors' abstract, as published at the source. Journal of Time Series Analysis, 2026 · DOI ↗
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Field: Signal Processing
Signal ProcessingComputer Science