PCA_FN

This function is to estimate factor numbers via eigenvalue ratios corresponding to Principal Component Analysis (PCA).

Factor models have been widely applied in areas such as economics and finance, and the well-known heavy-tailedness of macroeconomic/financial data should be taken into account when conducting factor analysis. We propose two algorithms to do robust factor analysis by considering the Huber loss. One is based on minimizing the Huber loss of the idiosyncratic error's L2 norm, which turns out to do Principal Component Analysis (PCA) on the weighted sample covariance matrix and thereby named as Huber PCA. The other one is based on minimizing the element-wise Huber loss, which can be solved by an iterative Huber regression algorithm. In this package we also provide the code for traditional PCA, the Robust Two Step (RTS) method by He et al. (2022) and the Quantile Factor Analysis (QFA) method by Chen et al. (2021) and He et al. (2023).

Dong Liu

HDRFA

High-Dimensional Robust Factor Analysis

Yong He

Lingxiao Li

Wenxin Zhou

PCA_FN function

<dl> <dt>X</dt>
<dd>Input matrix, of dimension \(T\times N\). Each row is an observation with \(N\) features at time point \(t\).</dd> <dt>rmax</dt>
<dd>The user-supplied maximum factor numbers.</dd></dl>

Arguments

Yong He, Lingxiao Li, Dong Liu, Wenxin Zhou.

Author

Estimating Factor Numbers via Eigenvalue Ratios Corresponding to PCA — PCA_FN

<dl>

 <dt>X</dt>
<dd>Input matrix, of dimension \(T\times N\). Each row is an observation with \(N\) features at time point \(t\).</dd>

 <dt>rmax</dt>
<dd>The user-supplied maximum factor numbers.</dd>

</dl>

PCA_FN: Estimating Factor Numbers via Eigenvalue Ratios Corresponding to PCA

Description

Usage

Value

Arguments

Author

Details

References

Examples