  Accurate estimation for extent of cross{sectional dependence in large panel
data analysis is paramount to further statistical analysis on the data under
study. Grouping more data with weak relations (cross{sectional dependence)
together often results in less efficient dimension reduction and worse
forecasting. This paper describes cross-sectional dependence among a large
number of objects (time series) via a factor model and parameterizes its extent
in terms of strength of factor loadings. A new joint estimation method,
benefiting from unique feature of dimension reduction for high dimensional time
series, is proposed for the parameter representing the extent and some other
parameters involved in the estimation procedure. Moreover, a joint asymptotic
distribution for a pair of estimators is established. Simulations illustrate
the effectiveness of the proposed estimation method in the finite sample
performance. Applications in cross-country macro-variables and stock returns
from S&P 500 are studied.
