DGP.CP {HDTSA} | R Documentation |
Generating simulated data for the example in Chang et al. (2024)
Description
DGP.CP()
function generates simulated data following the
data generating process described in Section 7.1 of Chang et al. (2024).
Usage
DGP.CP(n, p, q, d, d1, d2)
Arguments
n |
Integer. The number of observations of the |
p |
Integer. The number of rows of |
q |
Integer. The number of columns of |
d |
Integer. The number of columns of the factor loading matrices |
d1 |
Integer. The rank of the |
d2 |
Integer. The rank of the |
Details
We generate
{\bf{Y}}_t = {\bf A \bf X}_t{\bf B}' + {\boldsymbol{\epsilon}}_t
for any t=1, \ldots, n
, where {\bf X}_t = {\rm diag}({\bf x}_t)
with {\bf x}_t = (x_{t,1},\ldots,x_{t,d})'
being a d \times 1
time series,
{\boldsymbol{\epsilon}}_t
is a p \times q
matrix white noise,
and {\bf A}
and {\bf B}
are, respectively, p\times d
and
q \times d
factor loading matrices. \bf A
, {\bf X}_t
, and \bf B
are generated based on the data generating process described in Section 7.1 of
Chang et al. (2024) and satisfy {\rm rank}({\bf A})=d_1
and
{\rm rank}({\bf B})=d_2
, 1 \le d_1, d_2 \le d
.
Value
A list containing the following components:
Y |
An |
A |
The |
B |
The |
X |
An |
References
Chang, J., Du, Y., Huang, G., & Yao, Q. (2024). Identification and estimation for matrix time series CP-factor models. arXiv preprint. doi:10.48550/arXiv.2410.05634.
See Also
Examples
p <- 10
q <- 10
n <- 400
d = d1 = d2 <- 3
data <- DGP.CP(n,p,q,d1,d2,d)
Y <- data$Y
## The first observation: Y_1
Y[1, , ]