HDSReg  R Documentation 
HDSReg()
considers a multivariate time series model which
represents a high dimensional vector process as a sum of three terms: a
linear regression of some observed regressors, a linear combination of some
latent and serially correlated factors, and a vector white noise:
{\bf
y}_t = {\bf Dz}_t + {\bf Ax}_t + {\boldsymbol {\epsilon}}_t,
where {\bf
y}_t
and {\bf z}_t
are, respectively, observable p\times 1
and
m \times 1
time series, {\bf x}_t
is an r \times 1
latent
factor process, {\boldsymbol{\epsilon}}_t \sim
\mathrm{WN}({\boldsymbol{0}},{\bf \Sigma}_{\epsilon})
is a white noise with
zero mean and covariance matrix {\bf \Sigma}_{\epsilon}
and
{\boldsymbol{\epsilon}}_t
is uncorrelated with ({\bf z}_t, {\bf
x}_t)
, {\bf D}
is an unknown regression coefficient matrix, and
{\bf A}
is an unknown factor loading matrix. This procedure proposed in
Chang, Guo and Yao (2015) aims to estimate the unknown regression coefficient
matrix {\bf D}
, the number of factors r
and the factor loading
matrix {\bf A}
.
HDSReg(Y, Z, D = NULL, lag.k = 1, twostep = FALSE)
Y 

Z 

D 
A 
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 
reg.coff.mat 
The estimated 
loading.mat 
The estimated 
lag.k 
the time lag used in function. 
method 
a character string indicating what method was performed. 
Chang, J., Guo, B. & Yao, Q. (2015). High dimensional stochastic regression with latent factors, endogeneity and nonlinearity, Journal of Econometrics, Vol. 189, pp. 297–312.
Factors
.
n < 400
p < 200
m < 2
r < 3
X < mat.or.vec(n,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)
X < cbind(x1,x2,x3)
X < t(X)
Z < mat.or.vec(m,n)
S1 < matrix(c(5/8,1/8,1/8,5/8),2,2)
Z[,1] < c(rnorm(m))
for(i in c(2:n)){
Z[,i] < S1%*%Z[, i1] + c(rnorm(m))
}
D < matrix(runif(p*m, 2, 2), ncol=m)
A < matrix(runif(p*r, 2, 2), ncol=r)
eps < mat.or.vec(n, p)
eps < matrix(rnorm(n*p), p, n)
Y < D %*% Z + A %*% X + eps
Y < t(Y)
Z < t(Z)
res1 < HDSReg(Y,Z,D,lag.k=2)
res2 < HDSReg(Y,Z,lag.k=2)
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