PC | R Documentation |
Perform PC estimation of the (2D) approximate factor model:
y_{it}=\boldsymbol{\lambda}_{i}^{\prime}\boldsymbol{F}_{t}+e_{it},
or in matrix notation:
\boldsymbol{Y}=\boldsymbol{F}\boldsymbol{\Lambda}^{\prime}+\boldsymbol{e}.
The factors \boldsymbol{F}
is estimated as \sqrt{T}
times the r
eigenvectors of
the matrix \boldsymbol{Y}\boldsymbol{Y}^{\prime}
corresponding to the r
largest eigenvalues in descending order, and the loading matrix is estimated by
\boldsymbol{\Lambda}=T^{-1}\boldsymbol{Y}^{\prime}\boldsymbol{F}
.
See e.g. Bai and Ng (2002).
PC(Y, r)
Y |
A |
r |
= the number of factors. |
A list containing the factors and factor loadings:
factor = a T \times r
matrix of the estimated factors.
loading = a N \times r
matrix of the estimated factor loadings.
Bai, J. and Ng, S., 2002. Determining the number of factors in approximate factor models. Econometrica, 70(1), pp.191-221.
# simulate data
T <- 100
N <- 50
r <- 2
F <- matrix(stats::rnorm(T * r, 0, 1), nrow = T)
Lambda <- matrix(stats::rnorm(N * r, 0, 1), nrow = N)
err <- matrix(stats::rnorm(T * N, 0, 1), nrow = T)
Y <- F %*% t(Lambda) + err
# estimation
est_PC <- PC(Y, r)
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