Factors  R Documentation 
Factors()
deals with factor modeling for highdimensional
time series proposed in Lam and Yao (2012):
{\bf y}_t = {\bf Ax}_t +
{\boldsymbol{\epsilon}}_t,
where {\bf x}_t
is an r \times 1
latent process with (unknown) r \leq p
, {\bf A}
is a p
\times r
unknown constant matrix, and {\boldsymbol{\epsilon}}_t \sim
\mathrm{WN}({\boldsymbol{\mu}}_{\epsilon}, {\bf \Sigma}_{\epsilon})
is a
vector white noise process. The number of factors r
and the factor
loadings {\bf A}
can be estimated in terms of an eigenanalysis for a
nonnegative definite matrix, and is therefore applicable when the dimension
of {\bf y}_t
is on the order of a few thousands. This function aims to
estimate the number of factors r
and the factor loading matrix
{\bf A}
.
Factors(Y, lag.k = 5, twostep = FALSE)
Y 

lag.k 
Time lag
where 
twostep 
Logical. If 
An object of class "factors" is a list containing the following components:
factor_num 
The estimated number of factors

loading.mat 
The estimated 
lag.k 
the time lag used in function. 
method 
a character string indicating what method was performed. 
Lam, C. & Yao, Q. (2012). Factor modelling for highdimensional time series: Inference for the number of factors, The Annals of Statistics, Vol. 40, pp. 694–726.
## Generate x_t
p < 400
n < 400
r < 3
X < mat.or.vec(n, r)
A < matrix(runif(p*r, 1, 1), ncol=r)
x1 < arima.sim(model=list(ar=c(0.6)), n=n)
x2 < arima.sim(model=list(ar=c(0.5)), n=n)
x3 < arima.sim(model=list(ar=c(0.3)), n=n)
eps < matrix(rnorm(n*p), p, n)
X < t(cbind(x1, x2, x3))
Y < A %*% X + eps
Y < t(Y)
fac < Factors(Y,lag.k=2)
r_hat < fac$factor_num
loading_Mat < fac$loading.mat
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