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[, i-1] + 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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