In this paper , we propose a new procedure to build a structural-factor model for a vector unit-root time series . For a p-dimensional unit-root process , we assume that each component consists of a set of common factors, which may be unit-root non-stationary, and a set of stationary components, which contain the cointegrations among the unit-root processes. To further reduce the dimensionality, we also postulate that the stationary part of the series is a nonsingular linear transformation of certain common factors and idiosyncratic white noise components as in Gao and Tsay (2019a, b) . The estimation of  linear loading spaces of the unit-root factors and the stationary components is achieved by an eigenanalysis of some nonnegative definite matrix , and the separation between the stationary factors and the white noises is based on an eigenanalysis and a projected principal component analysis . Asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n tends to infinity. Both simulated and real examples are used to demonstrate the performance of the proposed method in finite samples  .
This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a p-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence . The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method for both fixed and diverging p as the sample size n increases, and use simulation and a real example to demonstrate the performance of the proposed method in finite samples . We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM_{2.5 .
R
In this paper , we propose
This paper proposes
R
a structural-factor model for a vector
factor models for high-dimensional
R
. For
by postulating that
R
, we assume that each component consists
is a nonsingular linear transformation
D
common factors, which may be
R
non-stationary, and
processes,
R
components, which contain the cointegrations among the unit-root processes. To further reduce the dimensionality, we also postulate that the stationary part of the series is a nonsingular linear transformation of certain common factors and
common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the
R
components as in Gao and Tsay (2019a, b)
series explains, jointly with the factors, the cross-sectional dependence
A
nonsingular
R
of the unit-root factors and the stationary components is achieved by
is carried out in two steps. First, we use
R
some
a
R
, and the separation between the stationary factors and the white noises is based on an
of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another
R
. Asymptotic
to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic
D
are established
D
p
R
tends to infinity. Both simulated and real examples are used
increases, and use simulation and a real example
A
. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM_{2.5